# 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**