  ### Home > CCA2 > Chapter 4 > Lesson 4.1.1 > Problem4-13

4-13.

Simplify each of the expressions below. Express your answers as simply as possible.

1. $\frac { 5 x ^ { 2 } - 11 x + 2 } { x ^ { 2 } + 8 x + 16 } \cdot \frac { x ^ { 2 } + 10 x + 24 } { 10 x ^ { 2 } + 13 x - 3 }$

Factor the polynomials, simplify, and then multiply.

$\frac{(x-2)(x+6)}{(x+4)(2x+3)}$

1. $\frac { 6 x + 3 } { 2 x - 3 } \div \frac { 3 x ^ { 2 } - 12 x - 15 } { 2 x ^ { 2 } - x - 3 }$

Factor the polynomials, simplify, and then divide.

Two of the polynomials have common factors.

1. $\frac { 5 m + 18 } { m + 3 } + \frac { 4 m + 9 } { m + 3 }$

Both fractions already have a common denominator, so add the fractions and then simplify by factoring.

$9$

1. $\frac { 3 a ^ { 2 } + a - 1 } { a ^ { 2 } - 2 a + 1 } - \frac { 2 a ^ { 2 } - a + 2 } { a ^ { 2 } - 2 a + 1 }$

Both fractions have a common denominator, so subtract the fractions.

$\frac{(3a^2+a-1)-(2a^2-a+2)}{a^2-2a+1}$

$\frac{ 3a^2 + a - 1 - 2a^2 +a -2 }{a^2 - 2a + 1}$

$\frac{a^2 + 2a -3}{a^2 - 2a + 1}$

$\frac{(a+3)(a-1)}{(a-1)(a-1)}$