# Fraction Equations Reducible to Quadratic | Free Math Help

\begin{aligned} \displaystyle \require{color} x+\frac{a}{x} &= b \\ x^2 + a &= bx \\ x^2 – bx + a &= 0 \\ \end{aligned}
Once, the equation forms a quadratic form by multiply the denominator to both sides, then the equation can be solved by quadratic solution, such as factorise or quadratic formula.
Let’s look at the following examples.

## Practice Questions

### Question 1

Solve $$\displaystyle x+\frac{2}{x} = 3$$.

### Question 2

Solve $$\displaystyle x^3 – \frac{8}{x^3} = 7$$.

### Question 3

Solve $$\displaystyle 16x^2 + \frac{16}{x^2} = 257$$.

### Question 4

Solve $$\displaystyle \sqrt{x} + \frac{1}{\sqrt{x}} = 2$$.