Algebra Examples

$b a - f b = f c$

Step 1

Subtract $f c$ from both sides of the equation.

$b a - f b - f c = 0$

Step 2

Subtract $b a$ from both sides of the equation.

$- f b - f c = - b a$

Step 3

Factor $f$ out of $- f b - f c$ .

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Step 3.1

Factor $f$ out of $- f b$ .

$f (- 1 b) - f c = - b a$

Step 3.2

Factor $f$ out of $- f c$ .

$f (- 1 b) + f (- 1 c) = - b a$

Step 3.3

Factor $f$ out of $f (- 1 b) + f (- 1 c)$ .

$f (- 1 b - 1 c) = - b a$

Step 4

Rewrite $- 1 b$ as $- b$ .

$f (- b - 1 c) = - b a$

Step 5

Rewrite $- 1 c$ as $- c$ .

$f (- b - c) = - b a$

Step 6

Divide each term in $f (- b - c) = - b a$ by $- b - c$ and simplify.

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Step 6.1

Divide each term in $f (- b - c) = - b a$ by $- b - c$ .

$\frac{f (- b - c)}{- b - c} = \frac{- b a}{- b - c}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $- b - c$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{f (- b - c)}{- b - c} = \frac{- b a}{- b - c}$

Step 6.2.1.2

Divide $f$ by $1$ .

$f = \frac{- b a}{- b - c}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Move the negative in front of the fraction.

$f = - \frac{b a}{- b - c}$

Step 6.3.2

Factor $- 1$ out of $- b$ .

$f = - \frac{b a}{- (b) - c}$

Step 6.3.3

Factor $- 1$ out of $- c$ .

$f = - \frac{b a}{- (b) - (c)}$

Step 6.3.4

Factor $- 1$ out of $- (b) - (c)$ .

$f = - \frac{b a}{- (b + c)}$

Step 6.3.5

Simplify the expression.

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Step 6.3.5.1

Rewrite $- (b + c)$ as $- 1 (b + c)$ .

$f = - \frac{b a}{- 1 (b + c)}$

Step 6.3.5.2

Move the negative in front of the fraction.

$f = - - \frac{b a}{b + c}$

Step 6.3.5.3

Multiply $- 1$ by $- 1$ .

$f = 1 \frac{b a}{b + c}$

Step 6.3.5.4

Multiply $\frac{b a}{b + c}$ by $1$ .

$f = \frac{b a}{b + c}$