Question

Could someone do this problemf or me? I'm havnig such a hard time. im horrible when it comes to showing my work.. I need all the work to be shown
x/x-2 + x-1/x+1 = -1

Answer 1

$\frac{x}{x-2} + \frac{x-1}{x+1} =1$
Least common denominator is (x-2)(x+1)
Multiply this times each term.
$(x-2)(x+1)( \frac{x}{x-2} )+(x-2)(x+1)( \frac{x-1}{x+1} )=(x-2)(x+1)(-1)$
After cancelling the like factors from numerator and denominator, you get
$(x+1)x+(x-2)(x-1)=(x-2)(x+1)(-1)$
Simplify the equation:
$x^2+x+x^2-3x+2=-x^2+x+2$
Add the opposite of all the terms on the right side to each side of the equation:
$3x^2-3x=0$
Factor out the GCF:
$3x(x-1)=0$
Set each factor equal to zero and solve:
$3x = 0$ or $x-1=0$
x = 0 or x = 1
After checking each answer in the original equation you will see both numbers work.  It's important to check because sometimes the answers can be extraneous (they don't work).