What is (12x-3y)/(15a+10b)*(21a+14b)/(20x-5y) ?

The solution to (12x-3y)/(15a+10b)*(21a+14b)/(20x-5y) is 21/25

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simplify (12x-3y)/(15a+10b)*(21a+14b)/(20x-5y)

simplify

\frac{12 x - 3 y}{15 a + 10 b} \cdot \frac{21 a + 14 b}{20 x - 5 y}

\frac{21}{25}

Solution steps

\frac{12 x - 3 y}{15 a + 10 b} \cdot \frac{21 a + 14 b}{20 x - 5 y}

Apply the fraction rule:

\frac{a}{b} \cdot \frac{c}{d} = \frac{a \cdot c}{b \cdot d}

= \frac{( 12 x - 3 y ) ( 21 a + 14 b )}{( 15 a + 10 b ) ( 20 x - 5 y )}

Factor

12 x - 3 y : 3 (4 x - y)

= \frac{3 ( 4 x - y ) ( 21 a + 14 b )}{( 15 a + 10 b ) ( 20 x - 5 y )}

Factor

20 x - 5 y : 5 (4 x - y)

= \frac{3 ( 4 x - y ) ( 21 a + 14 b )}{( 15 a + 10 b ) \cdot 5 ( 4 x - y )}

Cancel the common factor:

4 x - y

= \frac{3 ( 21 a + 14 b )}{( 15 a + 10 b ) \cdot 5}

Factor

21 a + 14 b : 7 (3 a + 2 b)

= \frac{3 \cdot 7 ( 3 a + 2 b )}{( 15 a + 10 b ) \cdot 5}

Factor

15 a + 10 b : 5 (3 a + 2 b)

= \frac{3 \cdot 7 ( 3 a + 2 b )}{5 ( 3 a + 2 b ) \cdot 5}

Cancel the common factor:

3 a + 2 b

= \frac{3 \cdot 7}{5 \cdot 5}

Multiply the numbers:

3 \cdot 7 = 21

= \frac{21}{5 \cdot 5}

Multiply the numbers:

5 \cdot 5 = 25

= \frac{21}{25}

1 \frac{1}{2} \cdot 3

- 1 + 6 x - 8 x + 4 - 2 x

\frac{y + 2}{( y + 2 ) ^{2}} \cdot \frac{y ^{2} - 4}{y}

\frac{( x ^{2} + 2 x )}{x}

\frac{x ^{2} + 8 x + 15}{x ^{2} - 9}

What is (12x-3y)/(15a+10b)*(21a+14b)/(20x-5y) ?
The solution to (12x-3y)/(15a+10b)*(21a+14b)/(20x-5y) is 21/25