Question

Find the value of $x:\frac{1}{x}+\frac{4}{5x}=\frac{2}{x+5}$

• A. $0.71$
• B. $3.57$
• C. $5.8$
• D. $45$

Answer 1

Answer: (D)

$45$

Given $\frac{2}{x+5}=\frac{1}{x}+\frac{4}{5x}$

Taking RHS:

$\frac{1}{x}+\frac{4}{5x}$

LCM is $5x$

$\Rightarrow \frac{5}{5x}+\frac{4}{5x}\Rightarrow \frac{9}{5x}$

Now taking LHS:

$\frac{2}{x+5}$

LHS $=$ RHS

$\frac{2}{x+5}=\frac{9}{5x}$

$\Rightarrow 5x\times 2=9(x+5)\Rightarrow 10x=9x+45\Rightarrow x=45$