Question

Solve the following equation for x.
*Attached file

Answer 1

How far have you gotten before getting stuck?

Answer 2

I started by multiplying both sides by the (√4x-3) base. That's about it

Answer 3

\[2\sqrt{x}-(\sqrt{4x}-3)=\frac{1}{\sqrt{4x}-3}\]Note that\[\sqrt{4x}=2\sqrt{x}\]Therefore we can rewrite the equation\[\cancel{2\sqrt{x}}-\cancel{2\sqrt{x}}+3=\frac{1}{2\sqrt{x}-3}\]Multiply both sides by the denominator\[3(2\sqrt{x}-3)=1\]\[6\sqrt{x}=10\]\[\sqrt{x}=\frac{10}{6}=\frac53\]\[x=\frac{5^2}{3^2}=\frac{25}{9}\]

Answer 4

x=5232=259