Manipulating Rational Expressions

a

x

, by multiplying both the numerator and the denominator by

x

. Then, we simplify the numerator and the denominator.

\frac{x + 3}{x}

\frac{a}{b} = \frac{a \cdot x}{b \cdot x}

\frac{( x + 3 ) x}{x \cdot x}

DistrDistribute

x

\frac{x \cdot x + 3 \cdot x}{x \cdot x}

\frac{x ^{2} + 3 x}{x ^{2}}

b

Let's do the same thing again.

\frac{x ^{2} + 7}{x + 1}

\frac{a}{b} = \frac{a \cdot x}{b \cdot x}

\frac{( x ^{2} + 7 ) \cdot x}{( x + 1 ) \cdot x}

DistrDistribute

x

\frac{x ^{2} \cdot x + 7 \cdot x}{x \cdot x + 1 \cdot x}

\frac{x ^{3} + 7 x}{x ^{2} + x}

Manipulating Rational Expressions 1.17 - Solution