### Home > CCA2 > Chapter 10 > Lesson 10.2.1 > Problem10-93

10-93.

Factor and simplify each expression below. Homework Help ✎

1. $\frac { x ^ { 2 } - 4 } { x ^ { 2 } + 4 x + 4 }$

2. $\frac { 2 x ^ { 2 } - 5 x - 3 } { 4 x ^ { 2 } + 4 x + 1 }$

3. Justify each step in simplifying the expression in part (a).

Factor and then reduce.

For the numerator, what numbers multiply to $-6$ and add to $-5?$

Put these numbers in a generic rectangle (these create your "middle term") along with the first and last terms.
Now find the greatest common factors of each row and column.

See the generic rectangle.
$2x^2 - 5x - 3 = (x - 3)(2x + 1)$

Now factor the denominator and simplify.