# How do you solve 7/x+3/4=5/x?

Sep 11, 2016

$x = - \frac{8}{3}$

#### Explanation:

We have: $\frac{7}{x} + \frac{3}{4} = \frac{5}{x}$

First, let's combine the fractions on the left-hand side of the equation:

$\implies \frac{28 + 3 x}{4 x} = \frac{5}{x}$

Then, let's cross-multiply:

$\implies x \left(28 + 3 x\right) = 5 \left(4 x\right)$

$\implies 3 {x}^{2} + 28 x = 20 x$

Now, let's subtract $20 x$ from both sides:

$\implies 3 {x}^{2} + 8 x = 0$

We can factorise to get:

$\implies x \left(3 x + 8\right) = 0$

$\implies x = 0$

or

$\implies 3 x + 8 = 0$

$\implies 3 x = - 8$

$\implies x = - \frac{8}{3}$

However, using $x = 0$ in the original equation would yield undefined values.

Therefore, the only real solution to the equation is $x = - \frac{8}{3}$.
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