Complex Fractions - PSAT Math

Card 0 of 3

Question

Simplify:

$\frac{1- \frac{2}{x}}{1+ \frac{2}{x^{2}}}$

Answer

Simplify the numerator and the denominator, then divide, as follows:

$\frac{1- \frac{2}{x}}{1+ \frac{2}{x^{2}}}$

$=\frac{\frac{1 \cdot x}{x} - \frac{2}{x}}{\frac{1 \cdot x^{2}}{x^{2}} + \frac{2}{x^{2}}}$

$=\frac{\frac{ x}{x} - \frac{2}{x}}{\frac{x^{2}}{x^{2}} + \frac{2}{x^{2}}}$

$=\frac{\frac{ x-2}{x} }{\frac{x^{2}+2}{x^{2}} }$

$= \frac{ x-2}{x} \div \frac{x^{2}+2}{x^{2}}$

$= \frac{ x-2}{x} \cdot \frac{x^{2}}{x^{2}+2}$

$= \frac{ x-2}{1} \cdot \frac{x }{x^{2}+2}$

$= \frac{ x^{2}-2x}{ x^{2}+2}$

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Question

Evaluate:

$\frac{3+\frac{1}{4}}{3-\frac{1}{4}}$

Answer

Simplify the numerator and the denominator, then divide, as follows:

$\frac{3+\frac{1}{4}}{3-\frac{1}{4}}$

$=\frac{ \frac{12}{4}+\frac{1}{4}}{\frac{12}{4}-\frac{1}{4}}$

$=\frac{ \frac{13}{4}}{\frac{11}{4} }$

$= \frac{13}{4}\div \frac{11}{4}$

$= \frac{13}{4}\cdot \frac{4}{11}$

$= \frac{13}{1}\cdot \frac{1}{11}$

$= \frac{13}{11}$

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Question

Solve:

$76-\frac{75}{6}=$

Answer

First reduce the fraction. We can divide both the numerator and the denominator by 3.

$\frac{75\div 3}{6\div 3}=\frac{25}{2}$

Now our expression looks like this:

$76-\frac{25}{2}$

When you add or subtract fractions, you need to have the same denominator. The lowest common deonminator here is 2. So we need to multiply and solve:

$\left ( \frac{2}{2}\right)\cdot76-\frac{25}{2}=\frac{152}{2}-\frac{25}{2}=\frac{127}{2}$

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