How to subtract rational expressions with different denominators

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PSAT Math › How to subtract rational expressions with different denominators

1 - 1

Simplify.

$\frac{x+5}{x}-\frac{2x-3}{x^{2}}$

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

CORRECT

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

$\frac{x+5}{x}-\frac{2x-3}{x^{2}}$

Determine an LCD (Least Common Denominator) between and $x^{2}$ .

LCD = $x^{2}$

$\frac{x(x+5)}{(x)x}-\frac{2x-3}{x^{2}}$

Multiply the top and bottom of the first rational expression by , so that the denominator will be $x^{2}$ .

Distribute the to .

$\frac{x^{2}+5x}{x^{2}}-\frac{2x-3}{x^{2}}$

Now you can subtract because both rational expressions have the same denominators.

$\frac{x^{2}+5x-2x+3}{x^{2}}$

Final Answer.

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