3/x-1-3x-2/x^2-1
This solution đơn hàng with adding, subtracting và finding the least common multiple.
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Step by Step Solution
Step 1 :
2 Simplify —— x2Equation at the kết thúc of step 1 : 3 2 (((— - 1) - 3x) - ——) - 1 x x2Step 2 :
3 Simplify — xEquation at the over of step 2 : 3 2 (((— - 1) - 3x) - ——) - 1 x x2Step 3 :
Rewriting the whole as an Equivalent Fraction :3.1Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator :1 1 • x 1 = — = ————— 1 x Equivalent fraction : The fraction thus generated looks different but has the same value as the whole Common denominator : The equivalent fraction & the other fraction involved in the calculation cốt truyện the same denominator
Adding fractions that have a common denominator :3.2 Adding up the two equivalent fractions địa chỉ cửa hàng the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
3 - (x) 3 - x ——————— = ————— x x Equation at the over of step 3 : (3 - x) 2 ((——————— - 3x) - ——) - 1 x x2
Step 4 :
Rewriting the whole as an Equivalent Fraction :4.1Subtracting a whole from a fraction Rewrite the whole as a fraction using x as the denominator :3x 3x • x 3x = —— = —————— 1 x Adding fractions that have a common denominator :4.2 Adding up the two equivalent fractions
(3-x) - (3x • x) -3x2 - x + 3 ———————————————— = ———————————— x x Equation at the end of step 4 : (-3x2 - x + 3) 2 (—————————————— - ——) - 1 x x2
Step 5 :
Step 6 :
Pulling out lượt thích terms :6.1 Pull out lượt thích factors:-3x2 - x + 3=-1•(3x2 + x - 3)Trying khổng lồ factor by splitting the middle term6.2Factoring 3x2 + x - 3 The first term is, 3x2 its coefficient is 3.The middle term is, +x its coefficient is 1.The last term, "the constant", is -3Step-1 : Multiply the coefficient of the first term by the constant 3•-3=-9Step-2 : Find two factors of -9 whose sum equals the coefficient of the middle term, which is 1.
| -9 | + | 1 | = | -8 | ||
| -3 | + | 3 | = | 0 | ||
| -1 | + | 9 | = | 8 |
Observation : No two such factors can be found !! Conclusion : Trinomial can not be factored
Calculating the Least Common Multiple :6.3 Find the Least Common Multiple The left denominator is : x The right denominator is : x2
| x | 1 | 2 | 2 |
Least Common Multiple: x2
Calculating Multipliers :6.4 Calculate multipliers for the two fractions Denote the Least Common Multiple by L.C.M Denote the Left Multiplier by Left_M Denote the Right Multiplier by Right_M Denote the Left Deniminator by L_Deno Denote the Right Multiplier by R_DenoLeft_M=L.C.M/L_Deno=xRight_M=L.C.M/R_Deno=1
Making Equivalent Fractions :6.5 Rewrite the two fractions into equivalent fractionsTwo fractions are called equivalent if they have the same numeric value. For example : một nửa and 2/4 are equivalent, y/(y+1)2 và (y2+y)/(y+1)3 are equivalent as well. Lớn calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (-3x2-x+3) • x —————————————————— = —————————————— L.C.M x2 R. Mult. • R. Num. 2 —————————————————— = —— L.C.M x2Adding fractions that have a common denominator :6.6 Adding up the two equivalent fractions
(-3x2-x+3) • x - (2) -3x3 - x2 + 3x - 2 ———————————————————— = —————————————————— x2 x2 Equation at the kết thúc of step 6 : (-3x3 - x2 + 3x - 2) ———————————————————— - 1 x2
Step 7 :
Rewriting the whole as an Equivalent Fraction :7.1Subtracting a whole from a fraction Rewrite the whole as a fraction using x2 as the denominator :1 1 • x2 1 = — = —————— 1 x2
Step 8 :
Pulling out like terms :8.1 Pull out lượt thích factors:-3x3 - x2 + 3x - 2=-1•(3x3 + x2 - 3x + 2)Checking for a perfect cube :8.23x3 + x2 - 3x + 2 is not a perfect cube
Trying to factor by pulling out :8.3 Factoring: 3x3 + x2 - 3x + 2 Thoughtfully split the expression at hand into groups, each group having two terms:Group 1: -3x + 2Group 2: 3x3 + x2Pull out from each group separately :Group 1: (-3x + 2) • (1) = (3x - 2) • (-1)Group 2: (3x + 1) • (x2)Bad news !! Factoring by pulling out fails : The groups have no common factor and can not be added up to form a multiplication.
Polynomial Roots Calculator :
8.4 Find roots (zeroes) of : F(x) = 3x3 + x2 - 3x + 2Polynomial Roots Calculator is a set of methods aimed at finding values ofxfor which F(x)=0 Rational Roots test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integersThe Rational Root Theorem states that if a polynomial zeroes for a rational numberP/Q then phường is a factor of the Trailing Constant và Q is a factor of the Leading CoefficientIn this case, the Leading Coefficient is 3 và the Trailing Constant is 2. The factor(s) are: of the Leading Coefficient : 1,3 of the Trailing Constant : 1 ,2 Let us demo ....
| -1 | 1 | -1.00 | 3.00 | ||||||
| -1 | 3 | -0.33 | 3.00 | ||||||
| -2 | 1 | -2.00 | -12.00 | ||||||
| -2 | 3 | -0.67 | 3.56 | ||||||
| 1 | 1 | 1.00 | 3.00 | ||||||
| 1 | 3 | 0.33 | 1.22 | ||||||
| 2 | 1 | 2.00 | 24.00 | ||||||
| 2 | 3 | 0.67 | 1.33 |
Polynomial Roots Calculator found no rational roots
Adding fractions that have a common denominator :8.5 Adding up the two equivalent fractions
(-3x3-x2+3x-2) - (x2) -3x3 - 2x2 + 3x - 2 ————————————————————— = ——————————————————— x2 x2
Step 9 :
Pulling out lượt thích terms :9.1 Pull out lượt thích factors:-3x3 - 2x2 + 3x - 2=-1•(3x3 + 2x2 - 3x + 2)Checking for a perfect cube :9.23x3 + 2x2 - 3x + 2 is not a perfect cube
Trying to lớn factor by pulling out :9.3 Factoring: 3x3 + 2x2 - 3x + 2 Thoughtfully split the expression at hand into groups, each group having two terms:Group 1: -3x + 2Group 2: 3x3 + 2x2Pull out from each group separately :Group 1: (-3x + 2) • (1) = (3x - 2) • (-1)Group 2: (3x + 2) • (x2)Bad news !! Factoring by pulling out fails : The groups have no common factor and can not be added up to khung a multiplication.
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Polynomial Roots Calculator :
9.4 Find roots (zeroes) of : F(x) = 3x3 + 2x2 - 3x + 2See theory in step 8.4 In this case, the Leading Coefficient is 3 và the Trailing Constant is 2. The factor(s) are: of the Leading Coefficient : 1,3 of the Trailing Constant : 1 ,2 Let us test ....
| -1 | 1 | -1.00 | 4.00 | ||||||
| -1 | 3 | -0.33 | 3.11 | ||||||
| -2 | 1 | -2.00 | -8.00 | ||||||
| -2 | 3 | -0.67 | 4.00 | ||||||
| 1 | 1 | 1.00 | 4.00 | ||||||
| 1 | 3 | 0.33 | 1.33 | ||||||
| 2 | 1 | 2.00 | 28.00 | ||||||
| 2 | 3 | 0.67 | 1.78 |
Polynomial Roots Calculator found no rational roots