### Home > AC > Chapter 10 > Lesson 10.1.2 > Problem10-21

10-21.

Simplify the expressions below.

1. $\frac{x^2-8x+16}{3x^2-10x-8}$ for $x\ne-\frac{2}{3}$ or $4$

Factor the numerator and denominator.

$\frac{\left(x-4\right)\left(x-4\right)}{\left(3x+2\right)\left(x-4\right)}$

After factoring, look for a Giant One to remove.

$\frac{x-4}{3x+2}$

2. $\frac{10x+25}{2x^2-x-15}$ for $x\ne-\frac{5}{2}$ or $3$

Refer to part (a).

3. $\frac{\left(k-4\right)\left(2k+1\right)}{5\left(2k+1\right)}\div\frac{\left(k-3\right)\left(k-4\right)}{10\left(k-3\right)}$ for $k\ne3$$4$, or $-\frac{1}{2}$

This is division with fractions. Here is a sample division problem with numbers.

$\frac{6}{5}\div\frac{24}{5}$

Rewrite as multiplication by taking the reciprocal of the divisor.

$\frac{6}{5}\cdot\frac{5}{24}$

Factor $24$ and use the Commutative Property to rewrite the problem so there are Giant Ones.

$\frac{5}{5}\cdot\frac{6\cdot1}{6\cdot4}$

Remove the Giant Ones.

$\frac{1}{4}$