Basic Math Examples

$\frac{6 u^{2} - 3 u + 4}{3 u^{2} + 5 u - 9} = 2$

Step 1

Find the LCD of the terms in the equation.

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Step 1.1

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

$3 u^{2} + 5 u - 9, 1$

Step 1.2

Remove parentheses.

$3 u^{2} + 5 u - 9, 1$

Step 1.3

The LCM of one and any expression is the expression.

$3 u^{2} + 5 u - 9$

Step 2

Multiply each term in

$\frac{6 u^{2} - 3 u + 4}{3 u^{2} + 5 u - 9} = 2$ by

$3 u^{2} + 5 u - 9$ to eliminate the fractions.

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Step 2.1

Multiply each term in

$\frac{6 u^{2} - 3 u + 4}{3 u^{2} + 5 u - 9} = 2$ by

$3 u^{2} + 5 u - 9$ .

$\frac{6 u^{2} - 3 u + 4}{3 u^{2} + 5 u - 9} (3 u^{2} + 5 u - 9) = 2 (3 u^{2} + 5 u - 9)$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

$3 u^{2} + 5 u - 9$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{6 u^{2} - 3 u + 4}{3 u^{2} + 5 u - 9} (3 u^{2} + 5 u - 9) = 2 (3 u^{2} + 5 u - 9)$

Step 2.2.1.2

Rewrite the expression.

$6 u^{2} - 3 u + 4 = 2 (3 u^{2} + 5 u - 9)$

Step 2.3

Simplify the right side.

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Step 2.3.1

Apply the distributive property.

$6 u^{2} - 3 u + 4 = 2 (3 u^{2}) + 2 (5 u) + 2 \cdot - 9$

Step 2.3.2

Simplify.

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Step 2.3.2.1

Multiply

$3$ by

$2$ .

$6 u^{2} - 3 u + 4 = 6 u^{2} + 2 (5 u) + 2 \cdot - 9$

Step 2.3.2.2

Multiply

$5$ by

$2$ .

$6 u^{2} - 3 u + 4 = 6 u^{2} + 10 u + 2 \cdot - 9$

Step 2.3.2.3

Multiply

$2$ by

$- 9$ .

$6 u^{2} - 3 u + 4 = 6 u^{2} + 10 u - 18$

Step 3

Solve the equation.

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Step 3.1

Move all terms containing

$u$ to the left side of the equation.

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Step 3.1.1

Subtract

$6 u^{2}$ from both sides of the equation.

$6 u^{2} - 3 u + 4 - 6 u^{2} = 10 u - 18$

Step 3.1.2

Subtract

$10 u$ from both sides of the equation.

$6 u^{2} - 3 u + 4 - 6 u^{2} - 10 u = - 18$

Step 3.1.3

Combine the opposite terms in

$6 u^{2} - 3 u + 4 - 6 u^{2} - 10 u$ .

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Step 3.1.3.1

Subtract

$6 u^{2}$ from

$6 u^{2}$ .

$- 3 u + 4 + 0 - 10 u = - 18$

Step 3.1.3.2

Add

$- 3 u + 4$ and

$0$ .

$- 3 u + 4 - 10 u = - 18$

Step 3.1.4

Subtract

$10 u$ from

$- 3 u$ .

$- 13 u + 4 = - 18$

Step 3.2

Move all terms not containing

$u$ to the right side of the equation.

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Step 3.2.1

Subtract

$4$ from both sides of the equation.

$- 13 u = - 18 - 4$

Step 3.2.2

Subtract

$4$ from

$- 18$ .

$- 13 u = - 22$

Step 3.3

Divide each term in

$- 13 u = - 22$ by

$- 13$ and simplify.

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Step 3.3.1

Divide each term in

$- 13 u = - 22$ by

$- 13$ .

$\frac{- 13 u}{- 13} = \frac{- 22}{- 13}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of

$- 13$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 13 u}{- 13} = \frac{- 22}{- 13}$

Step 3.3.2.1.2

Divide

$u$ by

$1$ .

$u = \frac{- 22}{- 13}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Dividing two negative values results in a positive value.

$u = \frac{22}{13}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$u = \frac{22}{13}$

Decimal Form:

$u = 1.\overline{692307}$

Mixed Number Form:

$u = 1 \frac{9}{13}$