Algebra Examples

$\frac{3}{m^{2}} = \frac{m - 4}{3 m^{2}} + \frac{2}{3 m^{2}}$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $\frac{m - 4}{3 m^{2}}$ from both sides of the equation.

$\frac{3}{m^{2}} - \frac{m - 4}{3 m^{2}} = \frac{2}{3 m^{2}}$

Step 1.2

Subtract $\frac{2}{3 m^{2}}$ from both sides of the equation.

$\frac{3}{m^{2}} - \frac{m - 4}{3 m^{2}} - \frac{2}{3 m^{2}} = 0$

Step 2

Simplify $\frac{3}{m^{2}} - \frac{m - 4}{3 m^{2}} - \frac{2}{3 m^{2}}$ .

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Step 2.1

Combine the numerators over the common denominator.

$\frac{3}{m^{2}} + \frac{- (m - 4) - 2}{3 m^{2}} = 0$

Step 2.2

Simplify each term.

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Step 2.2.1

Apply the distributive property.

$\frac{3}{m^{2}} + \frac{- m - - 4 - 2}{3 m^{2}} = 0$

Step 2.2.2

Multiply $- 1$ by $- 4$ .

$\frac{3}{m^{2}} + \frac{- m + 4 - 2}{3 m^{2}} = 0$

Step 2.3

Subtract $2$ from $4$ .

$\frac{3}{m^{2}} + \frac{- m + 2}{3 m^{2}} = 0$

Step 2.4

To write $\frac{3}{m^{2}}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{3}{m^{2}} \cdot \frac{3}{3} + \frac{- m + 2}{3 m^{2}} = 0$

Step 2.5

Write each expression with a common denominator of $3 m^{2}$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.5.1

Multiply $\frac{3}{m^{2}}$ by $\frac{3}{3}$ .

$\frac{3 \cdot 3}{m^{2} \cdot 3} + \frac{- m + 2}{3 m^{2}} = 0$

Step 2.5.2

Move $3$ to the left of $m^{2}$ .

$\frac{3 \cdot 3}{3 m^{2}} + \frac{- m + 2}{3 m^{2}} = 0$

Step 2.6

Combine the numerators over the common denominator.

$\frac{3 \cdot 3 - m + 2}{3 m^{2}} = 0$

Step 2.7

Simplify the numerator.

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Step 2.7.1

Multiply $3$ by $3$ .

$\frac{9 - m + 2}{3 m^{2}} = 0$

Step 2.7.2

Add $9$ and $2$ .

$\frac{- m + 11}{3 m^{2}} = 0$

Step 2.8

Factor $- 1$ out of $- m$ .

$\frac{- (m) + 11}{3 m^{2}} = 0$

Step 2.9

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{- (m) - 1 (- 11)}{3 m^{2}} = 0$

Step 2.10

Factor $- 1$ out of $- (m) - 1 (- 11)$ .

$\frac{- (m - 11)}{3 m^{2}} = 0$

Step 2.11

Rewrite $- (m - 11)$ as $- 1 (m - 11)$ .

$\frac{- 1 (m - 11)}{3 m^{2}} = 0$

Step 2.12

Move the negative in front of the fraction.

$- \frac{m - 11}{3 m^{2}} = 0$

Step 3

Set the numerator equal to zero.

$m - 11 = 0$

Step 4

Add $11$ to both sides of the equation.

$m = 11$