Algebra Examples

$3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} + 6 x^{- \frac{1}{2}}$

Step 1

Factor $3$ out of $3 x^{\frac{3}{2}} - 9 x^{\frac{1}{2}} + 6 x^{- \frac{1}{2}}$ .

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Step 1.1

Factor $3$ out of $3 x^{\frac{3}{2}}$ .

$3 (x^{\frac{3}{2}}) - 9 x^{\frac{1}{2}} + 6 x^{- \frac{1}{2}}$

Step 1.2

Factor $3$ out of $- 9 x^{\frac{1}{2}}$ .

$3 (x^{\frac{3}{2}}) + 3 (- 3 x^{\frac{1}{2}}) + 6 x^{- \frac{1}{2}}$

Step 1.3

Factor $3$ out of $6 x^{- \frac{1}{2}}$ .

$3 (x^{\frac{3}{2}}) + 3 (- 3 x^{\frac{1}{2}}) + 3 (2 x^{- \frac{1}{2}})$

Step 1.4

Factor $3$ out of $3 (x^{\frac{3}{2}}) + 3 (- 3 x^{\frac{1}{2}})$ .

$3 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}}) + 3 (2 x^{- \frac{1}{2}})$

Step 1.5

Factor $3$ out of $3 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}}) + 3 (2 x^{- \frac{1}{2}})$ .

$3 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + 2 x^{- \frac{1}{2}})$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + 2 \frac{1}{x^{\frac{1}{2}}})$

Step 3

Combine $2$ and $\frac{1}{x^{\frac{1}{2}}}$ .

$3 (x^{\frac{3}{2}} - 3 x^{\frac{1}{2}} + \frac{2}{x^{\frac{1}{2}}})$