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

7xx+1+8x-1-14×2-1
Simplify the denominator.
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)
Write each expression with a common denominator of (x+1)(x-1), by multiplying each by an appropriate factor of 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)
Simplify the numerator.
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)
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)
Simplify the numerator.
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 of 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)

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