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## Precalculus

### Course: Precalculus>Unit 4

Lesson 1: Reducing rational expressions to lowest terms

# Reduce rational expressions to lowest terms: Error analysis

## Problem

Raiden tried to reduce the following expression to lowest terms:
start fraction, 4, x, squared, minus, 12, x, divided by, 3, x, squared, plus, 15, x, end fraction
This is his work:
Factoring the numerator: 4, x, squared, minus, 12, x, equals, 4, x, left parenthesis, x, minus, 3, right parenthesis
Factoring the denominator: 3, x, squared, plus, 15, x, equals, 3, x, left parenthesis, x, plus, 5, right parenthesis
Reducing to lowest terms:
\begin{aligned} \dfrac{4x^2-12x}{3x^2+15x}&=\dfrac{4\cancel x(x-3)}{3\cancel x(x+5)} \\\\ &=\dfrac{4(x-3)}{3(x+5)} \end{aligned}
Finding excluded values: x, does not equal, minus, 5
What mistake did Raiden make?