Chapter 11.1, Problem 3P

(a)

To determine

Find the simplified form of the expression and state any excluded values.

Answer to Problem 3P

  $\text{a:}\frac{2x-5}{5-2x}=-1$

Explanation of Solution

Given: $\text{a:}\frac{2x-5}{5-2x}$

Concept Used:

Simplification of rational expression means cancel out the common factors from the numerator and denominator.

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify

Calculation:

  $\text{a:}\frac{2x-5}{5-2x}=\frac{2x-5}{-1(2x-5)}=-1[\text{Rule:}b-a=-1(a-b)]$; No excluded value.

Thus, $\text{a:}\frac{2x-5}{5-2x}=-1$

(b)

To determine

Find the simplified form of the expression and state any excluded values.

Answer to Problem 3P

  $\text{b:}\frac{y^2-16}{4-y}=-(y+4)$

Explanation of Solution

Given: $\text{b:}\frac{y^2-16}{4-y}$

Concept Used:

Simplification of rational expression means cancel out the common factors from the numerator and denominator.

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify

Calculation:

  $\text{b:}\frac{y^2-16}{4-y}=\frac{(y+4)(y-4)}{-1(y-4)}=-(y+4)$; No excluded value.

Thus, $\text{b:}\frac{y^2-16}{4-y}=-(y+4)$

(c)

To determine

Find the simplified form of the expression and state any excluded values.

Answer to Problem 3P

  $\text{c:}\frac{3-9d}{6d^2+d-1}=\frac{-3}{2d+1}$

Explanation of Solution

Given: $\text{c:}\frac{3-9d}{6d^2+d-1}$

Concept Used:

Simplification of rational expression means cancel out the common factors from the numerator and denominator.

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify

Calculation:

  $\text{c:}\frac{3-9d}{6d^2+d-1}=\frac{-3(3d-1)}{(3d-1)(2d+1)}=\frac{-3}{2d+1}$ ; Excluded value: $2d+1\ne 0\Rightarrow d\ne -\frac{1}{2}$

Thus, $\text{c:}\frac{3-9d}{6d^2+d-1}=\frac{-3}{2d+1}$

(d)

To determine

Find the simplified form of the expression and state any excluded values.

Answer to Problem 3P

  $\text{d:}\frac{3-3z}{2z^2-2}=\frac{-3}{2(z+1)}$

Explanation of Solution

Given: $\text{d:}\frac{3-3z}{2z^2-2}$

Concept Used:

Simplification of rational expression means cancel out the common factors from the numerator and denominator.

In any rational function, the denominator cannot be zero.

To find the excluded value of the function, make denominator equal to zero and simplify

Calculation:

  $\text{d:}\frac{3-3z}{2z^2-2}=\frac{-3(z-1)}{2(z+1)(z-1)}=\frac{-3}{2(z+1)}$ ; Excluded value: $z+1\ne 0\Rightarrow z\ne -1$

Thus, $\text{d:}\frac{3-3z}{2z^2-2}=\frac{-3}{2(z+1)}$