Solving Equations with Algebraic Fractions Flashcards

All 5 cards in this deck

What is the first step in solving an equation containing algebraic fractions?

Multiply every term by the common denominator to clear the fractions.

What are the steps to solve an equation containing algebraic fractions?

e.g. $\frac{2}{x}+\frac{3}{x+1}=2$

1. Multiply every term by $x(x+1)$: $2(x+1)+3x=2x(x+1)$
2. Expand and rearrange to $=0$: $2x^2-3x-2=0$
3. Solve the quadratic: $x=2$ or $x=-\frac{1}{2}$

What does cross-multiplying give for the equation $\frac{a}{b}=\frac{c}{d}$?

e.g. $\frac{2}{x+1}=\frac{3}{x-2}$

$ad=bc$

e.g. $2(x-2)=3(x+1)$

True or false? A value of $x$ that makes one of the denominators zero can still be a solution of the equation.

False. It must be rejected, because the fraction would be undefined.

True or false? Clearing the fractions in an equation with algebraic fractions always leaves a linear equation.

False. It often leaves a quadratic equation, which may have two solutions.