Question

identify the values that make the rational expressions below undefined.
*5. \\(\frac{25}{x + 10}\\)
*6. \\(\frac{12 + 3x}{5 - x}\\)

1. what is 14% of 120?
2. what is 75% of 60?
3. a school needs to raise $2700. a nearby store promises to donate twice the amount the students raise. how much money do the students need to raise?
4. ann - marie has $2.55 in nickels and dimes. she has $1.80 in dimes. how many nickels does ann - marie have?

a. write an equation to represent the situation.
b. how many nickels does she have?

Explanation:

Problem 5: $\boldsymbol{\frac{25}{x + 10}}$

Step1: Recall when rational expression is undefined

A rational expression is undefined when its denominator is zero. So, set the denominator equal to zero:
$x + 10 = 0$

Step2: Solve for $x$

Subtract 10 from both sides:
$x = -10$

Step1: Set denominator to zero (undefined condition)

Denominator: $5 - x = 0$

Step2: Solve for $x$

Add $x$ to both sides:
$5 = x$ or $x = 5$

Step1: Convert percentage to decimal

14% = $0.14$

Step2: Multiply by 120

$0.14 \times 120 = 16.8$

Answer:

$x = -10$

Problem 6: $\boldsymbol{\frac{12 + 3x}{5 - x}}$