Question
Make $a$ the subject of formula $x=\sqrt{\frac{a+b}{a-b}}$
✓
Answer
$x=\sqrt{\frac{a+b}{a-b}}$
Squaring both sides
$\Rightarrow x^2=\frac{a+b}{a-b} $
$\Rightarrow x^2(a-b)=a+b $
$\Rightarrow x^2 a-x^2 b=a+b $
$\Rightarrow x^2 a-a=b+x^2 b $
$\Rightarrow a\left(x^2-1\right)=b\left(x^2+1\right) $
$\Rightarrow a=\frac{b\left(x^2+1\right)}{\left(x^2-1\right)} .$
Squaring both sides
$\Rightarrow x^2=\frac{a+b}{a-b} $
$\Rightarrow x^2(a-b)=a+b $
$\Rightarrow x^2 a-x^2 b=a+b $
$\Rightarrow x^2 a-a=b+x^2 b $
$\Rightarrow a\left(x^2-1\right)=b\left(x^2+1\right) $
$\Rightarrow a=\frac{b\left(x^2+1\right)}{\left(x^2-1\right)} .$
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