Download Problem Solving Using Systems of Equations

Math 30-2
Rational Expressions & Equations
Rationals Review
For the Rational Expressions & Equations Unit Exam, you need to know how to:
 Find NPV’s of a rational expression.
1. State the non-permissible values of
y6
.
y 2  49
 Write equivalent rational expressions.
24 x 3  6 x
?
18 x 2
4x 2  6
36 x  144 x 3
C.
D.
3x
 108 x 2
2. Which of the following expressions is/are equivalent to
A.
4x 2
3x
B.
8x 3  2 x
6x 2
 Simplify rational expressions.
- Factor
- Cancel common factors (including variables, coefficients, and binomials)
3. Simplify the following rational expressions. State NPV’s.
x2
4  x2
a)
b)
3x  6
4 x 2  32 x 3
 Multiply and divide rational expressions.
- Factor
- If dividing, flip over second fraction and change to multiplying (remember: this
creates new NPV’s)
- Multiply straight across the top and bottom (leave binomials factored)
- Cancel common factors (including variables, coefficients, and binomials)
- You DO NOT need a common denominator
Math 30-2
Rational Expressions & Equations
4. Multiply or divide the following rational expressions. State NPV’s.
5 15k 4
6 x 2  15 x
a)
b)

 2x  5
4x
9k 2 20k
 Add and subtract rational expressions.
- Factor denominators
- You DO need a common denominator
- Write each fraction as an equivalent expression over the common denominator
- Add/subtract the numerators
- (Simplify if possible)
5. Add or subtract the following rational expressions. State NPV’s.
5x 2 x  9
y7
2


a)
b)
2
3x
6
4y  9 2y  3
Math 30-2
Rational Expressions & Equations
 Solve a rational equations with one term on each side of the = sign.
- Cross-multiply
- Solve the resulting equation (may be quadratic!)
- Reject extraneous roots
n
4

6. Solve the equation
.
n4 n2
 Solve a rational equations with more than one term on one side of the = sign.
- Factor denominators
- Find the LCD
- Multiply every numerator by the LCD
- Solve the resulting equation (may be quadratic!)
- Reject extraneous roots
5x
5
 3
7. Solve the equation
.
2x  4
x2
Math 30-2
Rational Expressions & Equations
 Model a real-life situation with a rational equation and solve.
8. Bill ordered two different types of tires for his garage. He spent $4500 on all-season tires
and $3500 on snow tires. Each all-season tire cost $8 less than a snow tire. He ordered
350 tires in total.
a) Let c = the cost of a snow tire. Write expressions for the number of snow tires and
the number of all-season tires Bill bought.
b) Write an equation using the expressions above that can be solved to find the price Bill
paid for each snow tire.
c) What are the reasonable restrictions on the variable in this situation? Explain.
d) Solve the equation to determine the price Bill paid for each snow tire and each allseason tire.