Question

Solve the following systems of equations:
$\frac{5}{x+1}-\frac{2}{y-1}=\frac{1}{2}$
$\frac{10}{x+1}+\frac{2}{y-1}=\frac{5}{2}$
where $x\ne -1$ and $y\ne 1$

Answer 1

Add both the equations ;

$\Rightarrow \frac{15}{x+1}=3$

$\Rightarrow x+1=5$

$\Rightarrow x=4$

Substituting x in equation 1, we get ;

$\Rightarrow 1-\frac{1}{2}=\frac{2}{y-1}$

$\Rightarrow y-1=4$

$\Rightarrow y=5$