Rational expressions

$\frac{1}{x}+\frac{1}{y}$

• A

  Add

• B

  Check your answer by plugging $x=2$ and $y=4$ into both my original expression, and your simplified expression. Do not use calculators or decimals.

$\frac{1}{x}–\frac{1}{y}=$

$\left(\frac{1}{x}\right)\left(\frac{1}{y}\right)=$

$\frac{\frac{1}{x}}{\frac{1}{y}}=$

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

• A

  Simplify

• B

  Check your answer by plugging $x=3$ into both my original expression, and your simplified expression. Do not use calculators or decimals.

• C

  Are there any x-values for which the new expression does not equal the old expression?

$\frac{2}{x^2-9}-\frac{4}{x^2+\mathrm{2x}-\text{15}}=$

$\frac{{\mathrm{4x}}^2-\text{25}}{x^2+\mathrm{2x}+1}\times \frac{x^2+\mathrm{4x}+3}{{\mathrm{2x}}^2+x-\text{15}}$

• A

  Multiply.

• B

  Check your answer by plugging $x=\mathrm{–2}$ into both my original expression, and your simplified expression. (If they don’t come out the same, you did something wrong!)

• C

  Are there any x-values for which the new expression does not equal the old expression?