Rational Equations and Variation

Explore solving rational equations, direct variation, inverse variation.

Lesson 5 of 53 parts Practice Flashcards

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Solving Rational Equations

Objective: Explain solving rational equations and use it to solve or interpret a problem.

Multiply by a valid common denominator, solve the resulting equation, and reject candidates that make any original denominator zero. Multiplication by an expression zero at an excluded input is not reversible there.

Worked examples

Try itRational Equations and Variation — practice 1.1: Solve 2/(x−5)=2/4.Show answer

Step 1: Assume x≠5 and divide by nonzero 2. Step 2: Set 1/(x−5)=1/4, so x−5=4. Step 3: Obtain x=9; check it is not excluded.

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Solving Rational Equations

Objective: Explain solving rational equations and use it to solve or interpret a problem.

Worked examples

Try itRational Equations and Variation — practice 1.1: Solve 2/(x−5)=2/4.Show answer

Step 1: Assume x≠5 and divide by nonzero 2. Step 2: Set 1/(x−5)=1/4, so x−5=4. Step 3: Obtain x=9; check it is not excluded.

Direct Variation

Objective: Explain direct variation and use it to solve or interpret a problem.

In direct variation y=kx, ratio y/x equals k for nonzero x and the graph passes through origin when x=0 is allowed. The constant of proportionality.

Worked examples

Try itRational Equations and Variation — practice 2.1: If y=3x, find y at x=8.Show answer

Step 1: Direct variation has y=kx with k=3. Step 2: Substitute x=8. Step 3: y=3(8)=24.

Inverse Variation

Objective: Explain inverse variation and use it to solve or interpret a problem.

In inverse variation y=k/x for x≠0, product xy=k; increasing positive x decreases y when k>0. No, division by zero is undefined.

Worked examples

Try itRational Equations and Variation — practice 3.1: If xy=44, find y when x=11.Show answer

Step 1: Inverse variation has xy=k. Step 2: Substitute x=11: 11y=44. Step 3: Divide by 11 to get y=4.

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