# How do you simplify (x^2 + 4x +4)/(x^2 + 7x +10) *( x^2 + 5x)/(x^2 + 6x + 8 )?

Jul 23, 2015

You first factorise and see what you can cancel

#### Explanation:

$= \frac{{\left(x + 2\right)}^{2}}{\left(x + 2\right) \left(x + 5\right)} \cdot \frac{x \left(x + 5\right)}{\left(x + 2\right) \left(x + 4\right)}$

We first note the restrictions $x \ne - 2 \mathmr{and} x \ne - 4 \mathmr{and} x \ne - 5$
as this would make denominator(s) $= 0$

Now we can cancel:

$= \frac{\cancel{\left(x + 2\right)} \left(x + 2\right)}{\cancel{\left(x + 2\right)} \left(x + 5\right)} \cdot \frac{x \left(x + 5\right)}{\left(x + 2\right) \left(x + 4\right)}$

$= \frac{x \cancel{\left(x + 2\right)} \cancel{\left(x + 5\right)}}{\cancel{\left(x + 2\right)} \left(x + 4\right) \cancel{\left(x + 5\right)}}$

$= \frac{x}{x + 4}$