Trigonometry Examples

$\frac{8 x - 4 y}{- 10 x + 5 y} = \frac{3}{9}$

Step 1

Factor each term.

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Step 1.1

Factor $4$ out of $8 x - 4 y$ .

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Step 1.1.1

Factor $4$ out of $8 x$ .

$\frac{4 (2 x) - 4 y}{- 10 x + 5 y} = \frac{3}{9}$

Step 1.1.2

Factor $4$ out of $- 4 y$ .

$\frac{4 (2 x) + 4 (- y)}{- 10 x + 5 y} = \frac{3}{9}$

Step 1.1.3

Factor $4$ out of $4 (2 x) + 4 (- y)$ .

$\frac{4 (2 x - y)}{- 10 x + 5 y} = \frac{3}{9}$

Step 1.2

Factor $5$ out of $- 10 x + 5 y$ .

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Step 1.2.1

Factor $5$ out of $- 10 x$ .

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

Step 1.2.2

Factor $5$ out of $5 y$ .

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

Step 1.2.3

Factor $5$ out of $5 (- 2 x) + 5 (y)$ .

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

Step 1.3

Cancel the common factor of $2 x - y$ and $- 2 x + y$ .

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Step 1.3.1

Factor $- 1$ out of $2 x$ .

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

Step 1.3.2

Factor $- 1$ out of $- y$ .

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

Step 1.3.3

Factor $- 1$ out of $- (- 2 x) - (y)$ .

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

Step 1.3.4

Rewrite $- (- 2 x + y)$ as $- 1 (- 2 x + y)$ .

$\frac{4 (- 1 (- 2 x + y))}{5 (- 2 x + y)} = \frac{3}{9}$

Step 1.3.5

Cancel the common factor.

$\frac{4 (- 1 (- 2 x + y))}{5 (- 2 x + y)} = \frac{3}{9}$

Step 1.3.6

Rewrite the expression.

$\frac{4 \cdot (- 1)}{5} = \frac{3}{9}$

Step 1.4

Simplify the numerator.

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Step 1.4.1

Multiply $4$ by $- 1$ .

$\frac{4 (- 1)}{5} = \frac{3}{9}$

Step 1.4.2

Multiply $4$ by $- 1$ .

$\frac{- 4}{5} = \frac{3}{9}$

Step 1.5

Move the negative in front of the fraction.

$- \frac{4}{5} = \frac{3}{9}$

Step 1.6

Cancel the common factor of $3$ and $9$ .

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Step 1.6.1

Factor $3$ out of $3$ .

$- \frac{4}{5} = \frac{3 (1)}{9}$

Step 1.6.2

Cancel the common factors.

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Step 1.6.2.1

Factor $3$ out of $9$ .

$- \frac{4}{5} = \frac{3 \cdot 1}{3 \cdot 3}$

Step 1.6.2.2

Cancel the common factor.

$- \frac{4}{5} = \frac{3 \cdot 1}{3 \cdot 3}$

Step 1.6.2.3

Rewrite the expression.

$- \frac{4}{5} = \frac{1}{3}$

Step 2

Since $- \frac{4}{5} \neq \frac{1}{3}$ , there are no solutions.

No solution