# Fraction Equations Reducible to Quadratic | Free Math Help

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

### Related Topics

Algebra Equations Reducible to Quadratic
Equations Reducible to Quadratic by Substitution
Exponential Equations Reducible to Quadratic
Logarithmic Equations Reducible to Quadratic
Trigonometric Equations Reducible to Quadratic
Surd Equations Reducible to Quadratic 