Question

Solve the following equation:
$\frac{3}{\sqrt{x+1}+1}+2\sqrt{x+1}=5$

Answer 1

$\frac{3}{\sqrt{x+1}+1}+2\sqrt{x+1}=5$

$3+2\sqrt{x+1}(\sqrt{x+1}+1)=5(\sqrt{x+1}+1)$

$3+2(x+1)+2\sqrt{x+1}=5\sqrt{x+1}+5$

$2x+5-5=3\sqrt{x+1}$

$2x=3\sqrt{x+1}$

${\left(2x\right)}^2={\left(3\sqrt{x+1}\right)}^2$

$4x^2=9x+9$

$4x^2-9x-9=0$

$4x^2-12x+3x-9=0$

$4x(x-3)+3(x-3)=0$

$(x-3)(4x+3)=0$

$x=3and\frac{-4}{3}$

$but\sqrt{x+1}cannotbe<0$

$hencex=3$