How do you multiply 1/8+2/x=17/(8x)?

May 14, 2015

There is nothing here to multiply.

Perhaps the question is about cross multiplying.

In order to cross multiply, we need to have a fraction equal to a fraction. So we'll need to get a single fraction on the left.

To get a single fraction on the left, we will need a common denominator, so we want:

$\frac{1}{8} + \frac{2}{x} = \frac{17}{8 x}$

$\frac{1}{8} \cdot \frac{x}{x} + \frac{2}{x} \cdot \frac{8}{8} = \frac{17}{8 x}$

$\frac{x}{8 x} + \frac{16}{8 x} = \frac{17}{8 x}$

$\frac{x + 16}{8 x} = \frac{17}{8 x}$

Now we can crossmultiply to get:

$8 x \left(x + 16\right) = 8 x \left(17\right)$

$8 {x}^{2} + 128 x = 136 x$

$8 {x}^{2} + 128 x - 136 x = 0$

$8 {x}^{2} - 8 x = 0$

$8 x \left(x - 1\right) = 0$

$x = 0$ is not possible in the original equation (It is an extraneous solution).

$x - 1 = 0$ gives the solution $x = 1$