Solving Linear Equations with Fractions (Leaving Cert Mathematics): Flashcards

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Solving Linear Equations with Fractions
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Best strategy for linear equations with fractions

Find LCD, then multiply through to eliminate all fractions

LCD meaning

Least Common Denominator

First step: linear equations with fractions

Find the least common denominator (LCD)

Technique to eliminate fractions from equation

Multiply every term by the LCD

Step after eliminating fractions

Collect like-terms

LCD of denominators 33, 44, 66

1212

Multiply by what when xx in denominator

xx

Solve: 2x3−54=x6+1\frac{2x}{3} - \frac{5}{4} = \frac{x}{6} + 1

x=92x = \frac{9}{2}

Solve: 3x+2=5x−1\frac{3}{x} + 2 = \frac{5}{x} - 1

x=23x = \frac{2}{3}

Final step after collecting like-terms

Solve for xx

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