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Author Jonathan David Author of Fiction
Author Jonathan David
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Solve Rational Equation by Clearing Fractions and Factoring | Sample from The Ultimate Crash Course Series

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Sample from The Ultimate Crash Course Series
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Solve Each Equation by Factoring (Rational Equation)

\frac{5}{x+4} = 4 + \frac{3}{x-2}

Step 1: Eliminate the Fractions

Find the common denominator and multiply both sides of the equation.

(x+4)(x-2)

(x+4)(x-2)\left[\frac{5}{x+4}=4+\frac{3}{x-2}\right]

Step 2: Multiply Through

\frac{5}{x+4}(x+4)(x-2)=4(x+4)(x-2)+\frac{3}{x-2}(x+4)(x-2)

5(x-2)=4(x+4)(x-2)+3(x+4)

Step 3: Expand

5x-10=4(x^2-2x+4x-8)+3x+12

5x-10=4(x^2+2x-8)+3x+12

5x-10=4x^2+8x-32+3x+12

Step 4: Collect Like Terms

0=4x^2+8x-32+3x+12-(5x-10)

4x^2+8x-32+3x+12-5x+10=0

4x^2+6x-10=0

Step 5: Factor

2x^2+3x-5=0

(2x+5)(x-1)=0

Final Answers

x=1,\quad x=-\frac{5}{2}

Important Note

This type of algebraic manipulation is essential for calculus. Calculus relies heavily on algebra skills such as factoring, clearing fractions, and collecting like terms.

Sample from The Ultimate Crash Course Series

This is a sample lesson from the Ultimate Crash Course Series. Get the full bundle of algebra, precalculus, calculus, and physics preparation material at Payhip. Students can also access over 1,000 lessons and podcasts through theSTEMmajor.com.

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