Question

simplify (√(x+h)-√x)/(h)=((1)/(√(x+h)+√x)

Answer 1

\[\frac{ \sqrt{x+h} -\sqrt{x} }{ h }=\frac{ 1 }{ \sqrt{x+h +\sqrt{x}} }\] We cross multiply: \[(\sqrt{x+h}-\sqrt{x})(\sqrt{x+h}+\sqrt{x})=h \] We have that (a-b)(a+b)=a²-b² so : \[(x+h)^{2}-x ^{2}=h\] Simplifying we get:

2xh+h²=h => h²+2xh-h=0 => h(h+2x-1)=0