Question

Help please?

((x+2)/(x-2)) - ((x-5)/(x^2-4))

I get (x^3 + x^2 + 3x - 18)/(x^3-2x^2-4x+8) ? But I can't simplify it. I know the other way is to just factor out the x^2 - 4 in the original equation, but the way I tried first should have technically worked too right?

Answer 1

\[\frac{x+2 }{x-2 }-\frac{ x-5}{ x ^{2}-4 }=\frac{ x+2 }{ x-2 }-\frac{ x-5 }{ x ^{2}-2^{2} }\]
\[=\frac{ x+2 }{ x-2 }-\frac{ x-5 }{ \left( x+2 \right)\left( x-2 \right) }\]

Answer 2

\[=\frac{ \left( x+2 \right)\left( x+2 \right)-\left( x-5 \right) }{\left( x+2 \right)\left( x-2 \right) }\]
\[=\frac{ x ^{2}+4x+4-x+5 }{\left( x+2 \right)\left( x-2 \right) }\]
I think you can solve further.

Answer 3

as you have done factorise numerator and denominator and cancel common factor x-2
from numerator and denominator.