Basic Math Examples

\frac{19 z}{2 z - 6} = \frac{y}{6 z - 18}

$\frac{19 z}{2 z - 6} = \frac{y}{6 z - 18}$

Step 1

Rewrite the equation as

\frac{y}{6 z - 18} = \frac{19 z}{2 z - 6}

$\frac{y}{6 z - 18} = \frac{19 z}{2 z - 6}$ .

\frac{y}{6 z - 18} = \frac{19 z}{2 z - 6}

$\frac{y}{6 z - 18} = \frac{19 z}{2 z - 6}$

Step 2

Multiply both sides by

6 z - 18

$6 z - 18$ .

\frac{y}{6 z - 18} (6 z - 18) = \frac{19 z}{2 z - 6} (6 z - 18)

$\frac{y}{6 z - 18} (6 z - 18) = \frac{19 z}{2 z - 6} (6 z - 18)$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Cancel the common factor of

6 z - 18

$6 z - 18$ .

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Step 3.1.1.1

Cancel the common factor.

$\frac{y}{6 z - 18} (6 z - 18) = \frac{19 z}{2 z - 6} (6 z - 18)$

Step 3.1.1.2

Rewrite the expression.

$y = \frac{19 z}{2 z - 6} (6 z - 18)$

$y = \frac{19 z}{2 z - 6} (6 z - 18)$

$y = \frac{19 z}{2 z - 6} (6 z - 18)$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify

$\frac{19 z}{2 z - 6} (6 z - 18)$ .

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Step 3.2.1.1

Simplify terms.

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Step 3.2.1.1.1

Factor

$2$ out of

$2 z - 6$ .

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Step 3.2.1.1.1.1

Factor

$2$ out of

$2 z$ .

$y = \frac{19 z}{2 (z) - 6} (6 z - 18)$

Step 3.2.1.1.1.2

Factor

$2$ out of

$- 6$ .

$y = \frac{19 z}{2 z + 2 \cdot - 3} (6 z - 18)$

Step 3.2.1.1.1.3

Factor

$2$ out of

$2 z + 2 \cdot - 3$ .

$y = \frac{19 z}{2 (z - 3)} (6 z - 18)$

$y = \frac{19 z}{2 (z - 3)} (6 z - 18)$

Step 3.2.1.1.2

Multiply

$\frac{19 z}{2 (z - 3)}$ by

$6 z - 18$ .

$y = \frac{19 z (6 z - 18)}{2 (z - 3)}$

Step 3.2.1.1.3

Cancel the common factor of

$6 z - 18$ and

$2$ .

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Step 3.2.1.1.3.1

Factor

$2$ out of

$19 z (6 z - 18)$ .

$y = \frac{2 (19 z (3 z - 9))}{2 (z - 3)}$

Step 3.2.1.1.3.2

Cancel the common factors.

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Step 3.2.1.1.3.2.1

Cancel the common factor.

$y = \frac{2 (19 z (3 z - 9))}{2 (z - 3)}$

Step 3.2.1.1.3.2.2

Rewrite the expression.

$y = \frac{19 z (3 z - 9)}{z - 3}$

$y = \frac{19 z (3 z - 9)}{z - 3}$

$y = \frac{19 z (3 z - 9)}{z - 3}$

$y = \frac{19 z (3 z - 9)}{z - 3}$

Step 3.2.1.2

Simplify the numerator.

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Step 3.2.1.2.1

Factor

$3$ out of

$3 z - 9$ .

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Step 3.2.1.2.1.1

Factor

$3$ out of

$3 z$ .

$y = \frac{19 z (3 (z) - 9)}{z - 3}$

Step 3.2.1.2.1.2

Factor

$3$ out of

$- 9$ .

$y = \frac{19 z (3 z + 3 \cdot - 3)}{z - 3}$

Step 3.2.1.2.1.3

Factor

$3$ out of

$3 z + 3 \cdot - 3$ .

$y = \frac{19 z (3 (z - 3))}{z - 3}$

$y = \frac{19 z \cdot 3 (z - 3)}{z - 3}$

Step 3.2.1.2.2

Multiply

$3$ by

$19$ .

$y = \frac{57 z (z - 3)}{z - 3}$

$y = \frac{57 z (z - 3)}{z - 3}$

Step 3.2.1.3

Cancel the common factor of

$z - 3$ .

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Step 3.2.1.3.1

Cancel the common factor.

$y = \frac{57 z (z - 3)}{z - 3}$

Step 3.2.1.3.2

Divide

$57 z$ by

$1$ .

$y = 57 z$

$y = 57 z$

$y = 57 z$

$y = 57 z$

$y = 57 z$

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