Checkpoint: Simplifying Rational Expressions with Multiplication and Division Solutions

Simplify. State when the given expression is undefined.

$\frac{x^{2} - 1}{7 x^{2} + 5 x - 2} \cdot \frac{21 x^{2} - 6 x}{10 x^{2} - 7 x - 3}$

$\frac{(x - 1) (x + 1)}{(7 x - 2) (x + 1)} \cdot \frac{3 x (7 x - 2)}{(10 x + 3) (x - 1)}$ $\begin{matrix} 7 x - 2 = 0 & x + 1 = 0 \\ x = \frac{2}{7} & x = - 1 \\ 10 x + 3 = 0 & x - 1 = 0 \\ x = - \frac{3}{10} & x = 1 \end{matrix}$

$\frac{3 x (x - 1) (x + 1) (7 x - 2)}{(7 x - 2) (x + 1) (10 x + 3) (x - 1)} \frac{3 x}{10 x + 3}, x \neq - 1, - \frac{3}{10}, \frac{2}{7}, 1$

Note

Because the expressions are being multiplied, only the denominators need to be set equal to zero to find the restrictions.

Q: Why is it not possible to simplify the terms “3x” and “+3” in the expression?
A: Because 3x is a monomial and “+3” is part of the binomial 10x + 3.