# Equations with algebraic fractions · Grade 9

> Equations with algebraic fractions, Grade 9: Values x cannot take and more. Explanation, worked examples and free practice following the Israeli curriculum.

In Equations with algebraic fractions (Grade 9) you practise 4 skills: Equations with numbers in the denominator · Values x cannot take · Solving equations with algebraic fractions · A solution that has to be rejected.

In an equation with an algebraic fraction, the unknown appears in a denominator. You cannot divide by zero, so first find the values x cannot take: those that make a denominator 0. Factorise a quadratic denominator first.

To solve, multiply both sides by the common denominator, so that the fractions disappear. Then solve the equation you get in the usual way.

Last, check every solution against the forbidden values. A solution that makes a denominator 0 is rejected. If every solution is rejected, the equation has no solution.

**Tip:** Write down the forbidden values before you multiply, and check against them at the end.

## What you learn

### Equations with numbers in the denominator

- Example: Solve: x ÷ 10 + 7 = 4
- Answer: −30
- Solution: Subtract 7 from both sides: x ÷ 10 = −3 Multiply both sides by 10: x = −3 × 10 = −30

### Values x cannot take

- Example: Which value of x is not allowed in 6 ÷ (2x + 14) ?
- Answer: −7
- Solution: 2x + 14 = 0 , so x = −7

### Solving equations with algebraic fractions

- Example: Solve: 36 ÷ (x − 3) = −6
- Answer: −3
- Solution: Not allowed: x = 3 . Multiply both sides by the denominator x − 3 : 36 = −6 × (x − 3) 36 = −6x + 18 −6x = 18 x = −3 The solution is allowed: it makes no denominator 0.

### A solution that has to be rejected

- Example: What is the solution of (x − 7) ÷ (x − 9) = 2 ÷ (x − 9) ?
- Options: No solution · x = 9
- Answer: No solution
- Solution: Not allowed: x = 9 , because then the denominator is 0. Multiply both sides by the denominator: x − 7 = 2 x = 9 But that is exactly the forbidden value, so the equation has no solution.

## Not on the site yet

- Equations with algebraic fractions and a parameter
- Inequalities with algebraic fractions

The exercises are made by rules and the answers are worked out in code. The topic follows the Israeli Ministry of Education's grade 9 maths curriculum (2026–27).

[Practise on the site](https://kixplo.com/il/en/) · [All Grade 9 topics](https://kixplo.com/il/en/math/grade-9/)