1. Equations & Inequalities

Rational Equations

1. Equations & Inequalities

# Rational Equations - Video Tutorials & Practice Problems

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## Introduction to Rational Equations

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2

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## Restrictions on Rational Equations

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3

Problem

ProblemSolve the equation. $\frac{2x+4}{x-1}=5$

A

$x=3$

B

$x=1$

C

$x=5$

D

No solution

4

Problem

ProblemSolve the equation. $\frac{5}{x}-\frac{2}{3x}=4+\frac{3}{x}$

A

$x=0$

B

$x=1$

C

$x=\frac13$

D

No solution

5

Problem

ProblemSolve the equation. $\frac{-5}{x+4}-3=\frac{x-1}{x+4}$

A

$x=4$

B

$x=1$

C

$x=-4$

D

No solution

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Additional resources for Rational Equations

PRACTICE PROBLEMS AND ACTIVITIES (30)

- In Exercises 1–26, solve and check each linear equation. 3(x - 1) = 21
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. (7x−4)/5x = 9/5 − ...
- In Exercises 1–14, simplify the expression or solve the equation, whichever is appropriate. 3(2x-5)-2(4x+1)=-...
- In Exercises 1–26, solve and check each linear equation. x - 5(x + 3) = 13
- Solve each equation. 5/6x - 2x+ 4/3=5/3
- In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 8/x²−9 + 4/x+3 = 2...
- In Exercises 1–26, solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)
- Solve each equation. -4(2x-6) +8x= 5x+24+x
- In Exercises 1–26, solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) -...
- In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equatio...
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2
- In Exercises 25-38, solve each equation. 3x/5 = 2x/3 +1
- In Exercises 1–34, solve each rational equation. If an equation has no solution, so state. 4/(x²+3x−10) + 1/(...
- Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - x = x/10...
- Determine whether each equation is an identity, a conditional equation, or a contradic-tion. Give the solution...
- Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the...
- Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the val...
- Solve each formula for the specified variable. Assume that the denominator is not 0 if variables appear in the...
- Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the val...
- Solve each equation for x. 3x=(2x-1)(m+4)
- In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5/(x + 4), y2 = 3/(x + 3), y3 ...
- In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equ...
- Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominat...
- The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each ...
- Evaluate x^2 - (xy - y) for x satisfying 3(x + 3)/5 = 2x + 6 and y satisfying - 2y - 10 = 5y + 18.
- Solve: x/(x−3)=2x/(x−3)−5/3
- In Exercises 99–106, solve each equation. - 2{7 - [4 -2(1 - x) + 3]} = 10 - [4x - 2(x - 3)]
- Solve: 3x-1/5 + x+2/2 = -3/10. (Section 1.4, Example 4)
- Find b such that (4x - b)/(x - 5) = 3 has a solution set given by {Ø}.