Basic Math Examples

$\frac{u}{42 - u} = \frac{3}{4}$

Step 1

Subtract $\frac{3}{4}$ from both sides of the equation.

$\frac{u}{42 - u} - \frac{3}{4} = 0$

Step 2

Simplify $\frac{u}{42 - u} - \frac{3}{4}$ .

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Step 2.1

To write $\frac{u}{42 - u}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{u}{42 - u} \cdot \frac{4}{4} - \frac{3}{4} = 0$

Step 2.2

To write $- \frac{3}{4}$ as a fraction with a common denominator, multiply by $\frac{42 - u}{42 - u}$ .

$\frac{u}{42 - u} \cdot \frac{4}{4} - \frac{3}{4} \cdot \frac{42 - u}{42 - u} = 0$

Step 2.3

Write each expression with a common denominator of $(42 - u) \cdot 4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.3.1

Multiply $\frac{u}{42 - u}$ by $\frac{4}{4}$ .

$\frac{u \cdot 4}{(42 - u) \cdot 4} - \frac{3}{4} \cdot \frac{42 - u}{42 - u} = 0$

Step 2.3.2

Multiply $\frac{3}{4}$ by $\frac{42 - u}{42 - u}$ .

$\frac{u \cdot 4}{(42 - u) \cdot 4} - \frac{3 (42 - u)}{4 (42 - u)} = 0$

Step 2.3.3

Reorder the factors of $(42 - u) \cdot 4$ .

$\frac{u \cdot 4}{4 (42 - u)} - \frac{3 (42 - u)}{4 (42 - u)} = 0$

Step 2.4

Combine the numerators over the common denominator.

$\frac{u \cdot 4 - 3 (42 - u)}{4 (42 - u)} = 0$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Move $4$ to the left of $u$ .

$\frac{4 \cdot u - 3 (42 - u)}{4 (42 - u)} = 0$

Step 2.5.2

Apply the distributive property.

$\frac{4 u - 3 \cdot 42 - 3 (- u)}{4 (42 - u)} = 0$

Step 2.5.3

Multiply $- 3$ by $42$ .

$\frac{4 u - 126 - 3 (- u)}{4 (42 - u)} = 0$

Step 2.5.4

Multiply $- 1$ by $- 3$ .

$\frac{4 u - 126 + 3 u}{4 (42 - u)} = 0$

Step 2.5.5

Add $4 u$ and $3 u$ .

$\frac{7 u - 126}{4 (42 - u)} = 0$

Step 2.5.6

Factor $7$ out of $7 u - 126$ .

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Step 2.5.6.1

Factor $7$ out of $7 u$ .

$\frac{7 (u) - 126}{4 (42 - u)} = 0$

Step 2.5.6.2

Factor $7$ out of $- 126$ .

$\frac{7 u + 7 \cdot - 18}{4 (42 - u)} = 0$

Step 2.5.6.3

Factor $7$ out of $7 u + 7 \cdot - 18$ .

$\frac{7 (u - 18)}{4 (42 - u)} = 0$