Basic Math Examples

$\frac{10 b + 5 b c - 6 c}{(7 b c - 4 b + c) (9 c - 8 b c)}$

Step 1

Factor $c$ out of $9 c - 8 b c$ .

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Step 1.1

Factor $c$ out of $9 c$ .

$\frac{10 b + 5 b c - 6 c}{(7 b c - 4 b + c) (c \cdot 9 - 8 b c)}$

Step 1.2

Factor $c$ out of $- 8 b c$ .

$\frac{10 b + 5 b c - 6 c}{(7 b c - 4 b + c) (c \cdot 9 + c (- 8 b))}$

Step 1.3

Factor $c$ out of $c \cdot 9 + c (- 8 b)$ .

$\frac{10 b + 5 b c - 6 c}{(7 b c - 4 b + c) (c (9 - 8 b))}$

$\frac{10 b + 5 b c - 6 c}{(7 b c - 4 b + c) c (9 - 8 b)}$

Step 2

Reorder factors in $\frac{10 b + 5 b c - 6 c}{(7 b c - 4 b + c) c (9 - 8 b)}$ .

$\frac{10 b + 5 b c - 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$

Step 3

Split the fraction $\frac{10 b + 5 b c - 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$ into two fractions.

$\frac{10 b + 5 b c}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{- 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$

Step 4

Split the fraction $\frac{10 b + 5 b c}{c (7 b c - 4 b + c) (9 - 8 b)}$ into two fractions.

$\frac{10 b}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{5 b c}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{- 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$

Step 5

Cancel the common factor of $c$ .

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Step 5.1

Cancel the common factor.

$\frac{10 b}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{5 b c}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{- 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$

Step 5.2

Rewrite the expression.

$\frac{10 b}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{5 b}{(7 b c - 4 b + c) (9 - 8 b)} + \frac{- 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$

Step 6

Cancel the common factor of $c$ .

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Step 6.1

Cancel the common factor.

$\frac{10 b}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{5 b}{(7 b c - 4 b + c) (9 - 8 b)} + \frac{- 6 c}{c (7 b c - 4 b + c) (9 - 8 b)}$

Step 6.2

Rewrite the expression.

$\frac{10 b}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{5 b}{(7 b c - 4 b + c) (9 - 8 b)} + \frac{- 6}{(7 b c - 4 b + c) (9 - 8 b)}$

Step 7

Move the negative in front of the fraction.

$\frac{10 b}{c (7 b c - 4 b + c) (9 - 8 b)} + \frac{5 b}{(7 b c - 4 b + c) (9 - 8 b)} - \frac{6}{(7 b c - 4 b + c) (9 - 8 b)}$