Basic Math Examples

$h = \frac{3 z + 7}{z - 5}$

Step 1

Multiply the equation by $z - 5$ .

$(z - 5) (h) = (\frac{3 z + 7}{z - 5}) (z - 5)$

Step 2

Simplify the left side.

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Step 2.1

Apply the distributive property.

$z h - 5 h = (\frac{3 z + 7}{z - 5}) (z - 5)$

Step 3

Simplify the right side.

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Step 3.1

Cancel the common factor of $z - 5$ .

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Step 3.1.1

Cancel the common factor.

$z h - 5 h = \frac{3 z + 7}{z - 5} (z - 5)$

Step 3.1.2

Rewrite the expression.

$z h - 5 h = 3 z + 7$

Step 4

Solve for $z$ .

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Step 4.1

Subtract $3 z$ from both sides of the equation.

$z h - 5 h - 3 z = 7$

Step 4.2

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

$z h - 3 z = 7 + 5 h$

Step 4.3

Factor $z$ out of $z h - 3 z$ .

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Step 4.3.1

Factor $z$ out of $z h$ .

$z (h) - 3 z = 7 + 5 h$

Step 4.3.2

Factor $z$ out of $- 3 z$ .

$z (h) + z \cdot - 3 = 7 + 5 h$

Step 4.3.3

Factor $z$ out of $z (h) + z \cdot - 3$ .

$z (h - 3) = 7 + 5 h$

Step 4.4

Divide each term in $z (h - 3) = 7 + 5 h$ by $h - 3$ and simplify.

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Step 4.4.1

Divide each term in $z (h - 3) = 7 + 5 h$ by $h - 3$ .

$\frac{z (h - 3)}{h - 3} = \frac{7}{h - 3} + \frac{5 h}{h - 3}$

Step 4.4.2

Simplify the left side.

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Step 4.4.2.1

Cancel the common factor of $h - 3$ .

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Step 4.4.2.1.1

Cancel the common factor.

$\frac{z (h - 3)}{h - 3} = \frac{7}{h - 3} + \frac{5 h}{h - 3}$

Step 4.4.2.1.2

Divide $z$ by $1$ .

$z = \frac{7}{h - 3} + \frac{5 h}{h - 3}$

Step 4.4.3

Simplify the right side.

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Step 4.4.3.1

Combine the numerators over the common denominator.

$z = \frac{7 + 5 h}{h - 3}$