7xx+1+8x-1-14×2-1

Rewrite 1 as 12.

7xx+1+8x-1-14×2-12

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=x and b=1.

7xx+1+8x-1-14(x+1)(x-1)

7xx+1+8x-1-14(x+1)(x-1)

To write 7xx+1 as a fraction with a common denominator, multiply by x-1x-1.

7xx+1⋅x-1x-1+8x-1-14(x+1)(x-1)

To write 8x-1 as a fraction with a common denominator, multiply by x+1x+1.

7xx+1⋅x-1x-1+8x-1⋅x+1x+1-14(x+1)(x-1)

Multiply 7xx+1 and x-1x-1.

7x(x-1)(x+1)(x-1)+8x-1⋅x+1x+1-14(x+1)(x-1)

Multiply 8x-1 and x+1x+1.

7x(x-1)(x+1)(x-1)+8(x+1)(x-1)(x+1)-14(x+1)(x-1)

Reorder the factors of (x-1)(x+1).

7x(x-1)(x+1)(x-1)+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

7x(x-1)(x+1)(x-1)+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

Combine the numerators over the common denominator.

7x(x-1)+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

Apply the distributive property.

7x⋅x+7x⋅-1+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

Multiply x by x by adding the exponents.

Move x.

7(x⋅x)+7x⋅-1+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

Multiply x by x.

7×2+7x⋅-1+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

7×2+7x⋅-1+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

Multiply -1 by 7.

7×2-7x+8(x+1)(x+1)(x-1)-14(x+1)(x-1)

Apply the distributive property.

7×2-7x+8x+8⋅1(x+1)(x-1)-14(x+1)(x-1)

Multiply 8 by 1.

7×2-7x+8x+8(x+1)(x-1)-14(x+1)(x-1)

Add -7x and 8x.

7×2+x+8(x+1)(x-1)-14(x+1)(x-1)

7×2+x+8(x+1)(x-1)-14(x+1)(x-1)

Combine the numerators over the common denominator.

7×2+x+8-14(x+1)(x-1)

Subtract 14 from 8.

7×2+x-6(x+1)(x-1)

Factor by grouping.

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=7⋅-6=-42 and whose sum is b=1.

Multiply by 1.

7×2+1x-6(x+1)(x-1)

Rewrite 1 as -6 plus 7

7×2+(-6+7)x-6(x+1)(x-1)

Apply the distributive property.

7×2-6x+7x-6(x+1)(x-1)

7×2-6x+7x-6(x+1)(x-1)

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

(7×2-6x)+7x-6(x+1)(x-1)

Factor out the greatest common factor (GCF) from each group.

x(7x-6)+1(7x-6)(x+1)(x-1)

x(7x-6)+1(7x-6)(x+1)(x-1)

Factor the polynomial by factoring out the greatest common factor, 7x-6.

(7x-6)(x+1)(x+1)(x-1)

(7x-6)(x+1)(x+1)(x-1)

(7x-6)(x+1)(x+1)(x-1)

Cancel the common factor.

(7x-6)(x+1)(x+1)(x-1)

Rewrite the expression.

7x-6x-1

7x-6x-1

Simplify (7x)/(x+1)+8/(x-1)-14/(x^2-1)