Precalculus Examples

$\frac{z + 2}{z - 3} = \frac{5}{- 3}$

Step 1

Move the negative in front of the fraction.

$\frac{z + 2}{z - 3} = - \frac{5}{3}$

Step 2

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.

$(z + 2) \cdot 3 = (z - 3) \cdot - 5$

Step 3

Solve the equation for $z$ .

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Step 3.1

Simplify $(z + 2) \cdot 3$ .

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Step 3.1.1

Rewrite.

$0 + 0 + (z + 2) \cdot 3 = (z - 3) \cdot - 5$

Step 3.1.2

Simplify by adding zeros.

$(z + 2) \cdot 3 = (z - 3) \cdot - 5$

Step 3.1.3

Apply the distributive property.

$z \cdot 3 + 2 \cdot 3 = (z - 3) \cdot - 5$

Step 3.1.4

Simplify the expression.

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Step 3.1.4.1

Move $3$ to the left of $z$ .

$3 \cdot z + 2 \cdot 3 = (z - 3) \cdot - 5$

Step 3.1.4.2

Multiply $2$ by $3$ .

$3 z + 6 = (z - 3) \cdot - 5$

Step 3.2

Simplify $(z - 3) \cdot - 5$ .

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Step 3.2.1

Apply the distributive property.

$3 z + 6 = z \cdot - 5 - 3 \cdot - 5$

Step 3.2.2

Simplify the expression.

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Step 3.2.2.1

Move $- 5$ to the left of $z$ .

$3 z + 6 = - 5 \cdot z - 3 \cdot - 5$

Step 3.2.2.2

Multiply $- 3$ by $- 5$ .

$3 z + 6 = - 5 z + 15$

Step 3.3

Move all terms containing $z$ to the left side of the equation.

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Step 3.3.1

Add $5 z$ to both sides of the equation.

$3 z + 6 + 5 z = 15$

Step 3.3.2

Add $3 z$ and $5 z$ .

$8 z + 6 = 15$

Step 3.4

Move all terms not containing $z$ to the right side of the equation.

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Step 3.4.1

Subtract $6$ from both sides of the equation.

$8 z = 15 - 6$

Step 3.4.2

Subtract $6$ from $15$ .

$8 z = 9$

Step 3.5

Divide each term in $8 z = 9$ by $8$ and simplify.

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Step 3.5.1

Divide each term in $8 z = 9$ by $8$ .

$\frac{8 z}{8} = \frac{9}{8}$

Step 3.5.2

Simplify the left side.

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Step 3.5.2.1

Cancel the common factor of $8$ .

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Step 3.5.2.1.1

Cancel the common factor.

$\frac{8 z}{8} = \frac{9}{8}$

Step 3.5.2.1.2

Divide $z$ by $1$ .

$z = \frac{9}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$z = \frac{9}{8}$

Decimal Form:

$z = 1.125$

Mixed Number Form:

$z = 1 \frac{1}{8}$