(x^2-7x-8)/(1-x^2)*(3x^2-4x+1)/(9x^2-1)

This solution deals with simplification or other simple results.

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Step by Step Solution

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Step 1 :

Equation at the over of step 1 : (((x2)-7x)-8) (((3•(x2))-4x)+1) —————————————•————————————————— (1-(x2)) (32x2-1)

Step 2 :

Equation at the over of step 2 : (((x2)-7x)-8) ((3x2-4x)+1) —————————————•———————————— (1-(x2)) (9x2-1)

Step 3 :

3x2 - 4x + 1 Simplify ———————————— 9x2 - 1 Trying khổng lồ factor by splitting the middle term3.1Factoring 3x2 - 4x + 1 The first term is, 3x2 its coefficient is 3.The middle term is, -4x its coefficient is -4.The last term, "the constant", is +1Step-1 : Multiply the coefficient of the first term by the constant 3•1=3Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -4.

-3+-1=-4That"s it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step2above, -3 & -13x2 - 3x-1x - 1Step-4 : add up the first 2 terms, pulling out like factors:3x•(x-1) add up the last 2 terms, pulling out common factors:1•(x-1) Step-5:Add up the four terms of step4:(3x-1)•(x-1)Which is the desired factorization

Trying to factor as a Difference of Squares:3.2 Factoring: 9x2-1 Theory : A difference of two perfect squares, A2-B2can be factored into (A+B)•(A-B)Proof:(A+B)•(A-B)= A2 - AB+BA-B2= A2 -AB+ AB - B2 = A2 - B2Note : AB = bố is the commutative property of multiplication. Chú ý : -AB+ AB equals zero & is therefore eliminated from the expression.Check: 9 is the square of 3Check: 1 is the square of 1Check: x2 is the square of x1Factorization is :(3x + 1)•(3x - 1)

Canceling Out :

3.3 Cancel out (3x - 1) which appears on both sides of the fraction line.

Equation at the kết thúc of step 3 :

(((x2)-7x)-8) (x-1) —————————————•————— (1-(x2)) 3x+1

Step 4 :

x2 - 7x - 8 Simplify ——————————— 1 - x2 Trying lớn factor by splitting the middle term4.1Factoring x2 - 7x - 8 The first term is, x2 its coefficient is 1.The middle term is, -7x its coefficient is -7.The last term, "the constant", is -8Step-1 : Multiply the coefficient of the first term by the constant 1•-8=-8Step-2 : Find two factors of -8 whose sum equals the coefficient of the middle term, which is -7.

-8+1=-7That"s it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step2above, -8 và 1x2 - 8x+1x - 8Step-4 : add up the first 2 terms, pulling out lượt thích factors:x•(x-8) add up the last 2 terms, pulling out common factors:1•(x-8) Step-5:Add up the four terms of step4:(x+1)•(x-8)Which is the desired factorization

Trying to lớn factor as a Difference of Squares:4.2 Factoring: 1-x2 Check: 1 is the square of 1Check: x2 is the square of x1Factorization is :(1 + x)•(1 - x)

Canceling Out :

4.3 Cancel out (x + 1) which appears on both sides of the fraction line.

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Equation at the end of step 4 :

(x - 8) (x - 1) ——————— • ——————— 1 - x 3x + 1

Step 5 :

5.1 Rewrite (1-x) as (-1) • (x-1)Canceling Out :5.2 Cancel out (x-1) which now appears on both sides of the fraction line.