Basic Math Examples

$\frac{i f (3 m + 2 y)}{5 m - 4 y} = \frac{9}{4}$

Step 1

Multiply the numerator of the first fraction by the denominator of the second fraction. Set this equal to the product of the denominator of the first fraction and the numerator of the second fraction.

$i f (3 m + 2 y) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2

Solve the equation for

$m$ .

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Step 2.1

Simplify

$i f (3 m + 2 y) \cdot 4$ .

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Step 2.1.1

Rewrite.

$0 + 0 + i f (3 m + 2 y) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.2

Simplify by multiplying through.

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Step 2.1.2.1

Apply the distributive property.

$(i f (3 m) + i f (2 y)) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.2.2

Reorder.

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Step 2.1.2.2.1

Rewrite using the commutative property of multiplication.

$(i \cdot 3 f m + i f (2 y)) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.2.2.2

Rewrite using the commutative property of multiplication.

$(i \cdot 3 f m + i \cdot 2 f y) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.3

Simplify each term.

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Step 2.1.3.1

Move

$3$ to the left of

$i$ .

$(3 \cdot i f m + i \cdot 2 f y) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.3.2

Move

$2$ to the left of

$i$ .

$(3 i f m + 2 i f y) \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.4

Simplify by multiplying through.

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Step 2.1.4.1

Apply the distributive property.

$3 i f m \cdot 4 + 2 i f y \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.4.2

Multiply.

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Step 2.1.4.2.1

Multiply

$4$ by

$3$ .

$12 i f m + 2 i f y \cdot 4 = (5 m - 4 y) \cdot 9$

Step 2.1.4.2.2

Multiply

$4$ by

$2$ .

$12 i f m + 8 i f y = (5 m - 4 y) \cdot 9$

Step 2.2

Simplify

$(5 m - 4 y) \cdot 9$ .

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Step 2.2.1

Apply the distributive property.

$12 i f m + 8 i f y = 5 m \cdot 9 - 4 y \cdot 9$

Step 2.2.2

Multiply.

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Step 2.2.2.1

Multiply

$9$ by

$5$ .

$12 i f m + 8 i f y = 45 m - 4 y \cdot 9$

Step 2.2.2.2

Multiply

$9$ by

$- 4$ .

$12 i f m + 8 i f y = 45 m - 36 y$

Step 2.3

Subtract

$45 m$ from both sides of the equation.

$12 i f m + 8 i f y - 45 m = - 36 y$

Step 2.4

Subtract

$8 i f y$ from both sides of the equation.

$12 i f m - 45 m = - 36 y - 8 i f y$

Step 2.5

Factor

$3 m$ out of

$12 i f m - 45 m$ .

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Step 2.5.1

Factor

$3 m$ out of

$12 i f m$ .

$3 m (4 i f) - 45 m = - 36 y - 8 i f y$

Step 2.5.2

Factor

$3 m$ out of

$- 45 m$ .

$3 m (4 i f) + 3 m (- 15) = - 36 y - 8 i f y$

Step 2.5.3

Factor

$3 m$ out of

$3 m (4 i f) + 3 m (- 15)$ .

$3 m (4 i f - 15) = - 36 y - 8 i f y$

Step 2.6

Divide each term in

$3 m (4 i f - 15) = - 36 y - 8 i f y$ by

$3 (4 i f - 15)$ and simplify.

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Step 2.6.1

Divide each term in

$3 m (4 i f - 15) = - 36 y - 8 i f y$ by

$3 (4 i f - 15)$ .

$\frac{3 m (4 i f - 15)}{3 (4 i f - 15)} = \frac{- 36 y}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of

$3$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{3 m (4 i f - 15)}{3 (4 i f - 15)} = \frac{- 36 y}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.2.1.2

Rewrite the expression.

$\frac{m (4 i f - 15)}{4 i f - 15} = \frac{- 36 y}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.2.2

Cancel the common factor of

$4 i f - 15$ .

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Step 2.6.2.2.1

Cancel the common factor.

$\frac{m (4 i f - 15)}{4 i f - 15} = \frac{- 36 y}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.2.2.2

Divide

$m$ by

$1$ .

$m = \frac{- 36 y}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Simplify each term.

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Step 2.6.3.1.1

Cancel the common factor of

$- 36$ and

$3$ .

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Step 2.6.3.1.1.1

Factor

$3$ out of

$- 36 y$ .

$m = \frac{3 (- 12 y)}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.1.1.2

Cancel the common factors.

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Step 2.6.3.1.1.2.1

Cancel the common factor.

$m = \frac{3 (- 12 y)}{3 (4 i f - 15)} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.1.1.2.2

Rewrite the expression.

$m = \frac{- 12 y}{4 i f - 15} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.1.2

Move the negative in front of the fraction.

$m = - \frac{12 y}{4 i f - 15} + \frac{- 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.1.3

Move the negative in front of the fraction.

$m = - \frac{12 y}{4 i f - 15} - \frac{8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.2

To write

$- \frac{12 y}{4 i f - 15}$ as a fraction with a common denominator, multiply by

$\frac{3}{3}$ .

$m = - \frac{12 y}{4 i f - 15} \cdot \frac{3}{3} - \frac{8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.3

Write each expression with a common denominator of

$(4 i f - 15) \cdot 3$ , by multiplying each by an appropriate factor of

$1$ .

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Step 2.6.3.3.1

Multiply

$\frac{12 y}{4 i f - 15}$ by

$\frac{3}{3}$ .

$m = - \frac{12 y \cdot 3}{(4 i f - 15) \cdot 3} - \frac{8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.3.2

Reorder the factors of

$(4 i f - 15) \cdot 3$ .

$m = - \frac{12 y \cdot 3}{3 (4 i f - 15)} - \frac{8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.4

Combine the numerators over the common denominator.

$m = \frac{- 12 y \cdot 3 - 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.5

Simplify the numerator.

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Step 2.6.3.5.1

Factor

$4 y$ out of

$- 12 y \cdot 3 - 8 i f y$ .

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Step 2.6.3.5.1.1

Factor

$4 y$ out of

$- 12 y \cdot 3$ .

$m = \frac{4 y (- 3 \cdot 3) - 8 i f y}{3 (4 i f - 15)}$

Step 2.6.3.5.1.2

Factor

$4 y$ out of

$- 8 i f y$ .

$m = \frac{4 y (- 3 \cdot 3) + 4 y (- 2 i f)}{3 (4 i f - 15)}$

Step 2.6.3.5.1.3

Factor

$4 y$ out of

$4 y (- 3 \cdot 3) + 4 y (- 2 i f)$ .

$m = \frac{4 y (- 3 \cdot 3 - 2 i f)}{3 (4 i f - 15)}$

Step 2.6.3.5.2

Multiply

$- 3$ by

$3$ .

$m = \frac{4 y (- 9 - 2 i f)}{3 (4 i f - 15)}$

Step 2.6.3.6

Simplify with factoring out.

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Step 2.6.3.6.1

Rewrite

$- 9$ as

$- 1 (9)$ .

$m = \frac{4 y (- 1 (9) - 2 i f)}{3 (4 i f - 15)}$

Step 2.6.3.6.2

Factor

$- 1$ out of

$- 2 i f$ .

$m = \frac{4 y (- 1 (9) - (2 i f))}{3 (4 i f - 15)}$

Step 2.6.3.6.3

Factor

$- 1$ out of

$- 1 (9) - (2 i f)$ .

$m = \frac{4 y (- 1 (9 + 2 i f))}{3 (4 i f - 15)}$

Step 2.6.3.6.4

Simplify the expression.

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Step 2.6.3.6.4.1

Move the negative in front of the fraction.

$m = - \frac{(4 y) (9 + 2 i f)}{3 (4 i f - 15)}$

Step 2.6.3.6.4.2

Reorder factors in

$- \frac{(4 y) (9 + 2 i f)}{3 (4 i f - 15)}$ .

$m = - \frac{4 y (9 + 2 i f)}{3 (4 i f - 15)}$