Basic Math Examples

4 = \frac{6}{u - 3}

$4 = \frac{6}{u - 3}$

Step 1

Rewrite the equation as

\frac{6}{u - 3} = 4

$\frac{6}{u - 3} = 4$ .

\frac{6}{u - 3} = 4

$\frac{6}{u - 3} = 4$

Step 2

Find the LCD of the terms in the equation.

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Step 2.1

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

u - 3, 1

$u - 3, 1$

Step 2.2

Remove parentheses.

u - 3, 1

$u - 3, 1$

Step 2.3

The LCM of one and any expression is the expression.

u - 3

$u - 3$

u - 3

$u - 3$

Step 3

Multiply each term in

\frac{6}{u - 3} = 4

$\frac{6}{u - 3} = 4$ by

u - 3

$u - 3$ to eliminate the fractions.

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Step 3.1

Multiply each term in

\frac{6}{u - 3} = 4

$\frac{6}{u - 3} = 4$ by

u - 3

$u - 3$ .

\frac{6}{u - 3} (u - 3) = 4 (u - 3)

$\frac{6}{u - 3} (u - 3) = 4 (u - 3)$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of

u - 3

$u - 3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{6}{u - 3} (u - 3) = 4 (u - 3)$

Step 3.2.1.2

Rewrite the expression.

$6 = 4 (u - 3)$

$6 = 4 (u - 3)$

$6 = 4 (u - 3)$

Step 3.3

Simplify the right side.

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Step 3.3.1

Apply the distributive property.

$6 = 4 u + 4 \cdot - 3$

Step 3.3.2

Multiply

$4$ by

$- 3$ .

$6 = 4 u - 12$

$6 = 4 u - 12$

$6 = 4 u - 12$

Step 4

Solve the equation.

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Step 4.1

Rewrite the equation as

$4 u - 12 = 6$ .

$4 u - 12 = 6$

Step 4.2

Move all terms not containing

$u$ to the right side of the equation.

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Step 4.2.1

Add

$12$ to both sides of the equation.

$4 u = 6 + 12$

Step 4.2.2

Add

$6$ and

$12$ .

$4 u = 18$

$4 u = 18$

Step 4.3

Divide each term in

$4 u = 18$ by

$4$ and simplify.

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Step 4.3.1

Divide each term in

$4 u = 18$ by

$4$ .

$\frac{4 u}{4} = \frac{18}{4}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of

$4$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{4 u}{4} = \frac{18}{4}$

Step 4.3.2.1.2

Divide

$u$ by

$1$ .

$u = \frac{18}{4}$

$u = \frac{18}{4}$

$u = \frac{18}{4}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Cancel the common factor of

$18$ and

$4$ .

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Step 4.3.3.1.1

Factor

$2$ out of

$18$ .

$u = \frac{2 (9)}{4}$

Step 4.3.3.1.2

Cancel the common factors.

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Step 4.3.3.1.2.1

Factor

$2$ out of

$4$ .

$u = \frac{2 \cdot 9}{2 \cdot 2}$

Step 4.3.3.1.2.2

Cancel the common factor.

$u = \frac{2 \cdot 9}{2 \cdot 2}$

Step 4.3.3.1.2.3

Rewrite the expression.

$u = \frac{9}{2}$

$u = \frac{9}{2}$

$u = \frac{9}{2}$

$u = \frac{9}{2}$

$u = \frac{9}{2}$

$u = \frac{9}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$u = \frac{9}{2}$

Decimal Form:

$u = 4.5$

Mixed Number Form:

$u = 4 \frac{1}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$