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Q.

If $\frac{5}{x + 3} = \frac{1}{x} + \frac{1}{2 x}$ , calculate the value of $x$ .

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a

\frac{4}{7}

b

\frac{2}{3}

c

\frac{9}{7}

d

\frac{5}{11}

answer is C.

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Detailed Solution

Given,

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

.
Simplifying, RHS =

\frac{1}{x} + \frac{1}{2 x}

.
LCM of these is

2 x

\Rightarrow \frac{2}{2 x} + \frac{1}{2 x}

\Rightarrow \frac{3}{2 x}

Now taking LHS =

\frac{5}{x + 3}

It is given, LHS

=

RHS
⇒

\frac{5}{x + 3} = \frac{3}{2 x}

\Rightarrow 5 \times 2 x = 3 \times (x + 3)

\Rightarrow 10 x = 3 x + 9

\Rightarrow x = \frac{9}{7}

Hence, the correct option is 3.

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