Solve for x
x = \frac{13}{2} = 6\frac{1}{2} = 6.5
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\left(x+1\right)\left(-1\right)=\left(x-5\right)\left(-5\right)
Variable x cannot be equal to any of the values -1,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x+1\right), the least common multiple of x-5,x+1.
-x-1=\left(x-5\right)\left(-5\right)
Use the distributive property to multiply x+1 by -1.
-x-1=-5x+25
Use the distributive property to multiply x-5 by -5.
-x-1+5x=25
Add 5x to both sides.
4x-1=25
Combine -x and 5x to get 4x.
4x=25+1
Add 1 to both sides.
4x=26
Add 25 and 1 to get 26.
x=\frac{26}{4}
Divide both sides by 4.
x=\frac{13}{2}
Reduce the fraction \frac{26}{4} to lowest terms by extracting and canceling out 2.
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