# How do you solve x+ 1/x = 10/3?

May 17, 2016

Put on a common denominator

#### Explanation:

$\frac{x \times x \times 3}{3 x} + \frac{1 \times 3}{3 x} = \frac{10 \times x}{3}$

Multiply and then you can clear the denominators and solve like a regular quadratic equation.

$3 {x}^{2} + 3 = 10 x$

$3 {x}^{2} - 10 x + 3 = 0$

$3 {x}^{2} - 9 x - x + 3 = 0$

$3 x \left(x - 3\right) - 1 \left(x - 3\right) = 0$

$\left(3 x - 1\right) \left(x - 3\right) = 0$

$x = \frac{1}{3} \mathmr{and} 3$

With rational equations, it's also important to note the restrictions on the variable.

There will be restrictions when the denominator is equal to 0, since in math division by 0 is undefined.

Therefore, $x \ne 0$

To summarize, $x = \frac{1}{3} \mathmr{and} 3 , x \ne 0$

Hopefully this helps!