Solve for f (k-g)/(f-7)=h

$\frac{k - g}{f - 7} = h$

Step 1

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$f - 7, 1$

Remove parentheses.

$f - 7, 1$

The LCM of one and any expression is the expression.

$f - 7$

Step 2

Multiply each term in $\frac{k - g}{f - 7} = h$ by $f - 7$ to eliminate the fractions.

Multiply each term in $\frac{k - g}{f - 7} = h$ by $f - 7$ .

$\frac{k - g}{f - 7} (f - 7) = h (f - 7)$

Simplify the left side.

Cancel the common factor of $f - 7$ .

Cancel the common factor.

$\frac{k - g}{f - 7} (f - 7) = h (f - 7)$

Rewrite the expression.

$k - g = h (f - 7)$

Simplify the right side.

Apply the distributive property.

$k - g = h f + h \cdot - 7$

Move $- 7$ to the left of $h$ .

$k - g = h f - 7 h$

Step 3

Solve the equation.

Rewrite the equation as $h f - 7 h = k - g$ .

$h f - 7 h = k - g$

Add $7 h$ to both sides of the equation.

$h f = k - g + 7 h$

Divide each term in $h f = k - g + 7 h$ by $h$ and simplify.

Divide each term in $h f = k - g + 7 h$ by $h$ .

$\frac{h f}{h} = \frac{k}{h} + \frac{- g}{h} + \frac{7 h}{h}$

Simplify the left side.

Cancel the common factor of $h$ .

Cancel the common factor.

$\frac{h f}{h} = \frac{k}{h} + \frac{- g}{h} + \frac{7 h}{h}$

Divide $f$ by $1$ .

$f = \frac{k}{h} + \frac{- g}{h} + \frac{7 h}{h}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$f = \frac{k}{h} - \frac{g}{h} + \frac{7 h}{h}$

Cancel the common factor of $h$ .

Cancel the common factor.

$f = \frac{k}{h} - \frac{g}{h} + \frac{7 h}{h}$

Divide $7$ by $1$ .

$f = \frac{k}{h} - \frac{g}{h} + 7$

Solve for f (k-g)/(f-7)=h

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