Cross-Multiplication and LCD

Algebra 2 · Axiom Academy

LESSON Cross-Multiplication and LCD Two ways to clear the fractions in a rational equation — cross-multiply when it's , use the LCD for sums — then reject any root that makes a denominator zero. When an equation is just one fraction equal to one fraction , you don't need a common denominator at all. Multiply diagonally across the equals sign — the numerator of each side times the denominator of the other. Multiply the diagonals — ad = bc Distribute and gather the x -terms Solve — and x=3 makes no denominator zero, so it holds As soon as there are more than two fractions , or fractions and whole numbers mixed together, cross-multiplication no longer applies. Instead, find the least common denominator of every term and multiply the entire equation by it — each denominator cancels, and the fractions disappear. The denominators are — their least common denominator Each denominator cancels — the fractions are gone Watch both candidates run back through the original denominator: one survives, the other collapses a denominator to zero. Factor x^2 - 4 = (x+2)(x-2) , so the LCD is Multiply every term by the LCD Both methods reach the same answer — pick by the shape of the equation, then finish with the one check they share. it's one fraction equal to one fraction, and you want the quickest route. there are three or more terms, fractions on the same side, or whole numbers mixed in:

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