What is (5m+25)/(14)*(7m+7)/(10m+50) ?

The solution to (5m+25)/(14)*(7m+7)/(10m+50) is (m+1)/4

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simplify (5m+25)/(14)*(7m+7)/(10m+50)

simplify

\frac{5 m + 25}{14} \cdot \frac{7 m + 7}{10 m + 50}

\frac{m + 1}{4}

Solution steps

\frac{5 m + 25}{14} \cdot \frac{7 m + 7}{10 m + 50}

Apply the fraction rule:

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

= \frac{( 5 m + 25 ) ( 7 m + 7 )}{14 ( 10 m + 50 )}

Factor

7 m + 7 : 7 (m + 1)

= \frac{( 5 m + 25 ) \cdot 7 ( m + 1 )}{14 ( 10 m + 50 )}

Factor the number:

14 = 7 \cdot 2

= \frac{( 5 m + 25 ) \cdot 7 ( m + 1 )}{7 \cdot 2 ( 10 m + 50 )}

Cancel the common factor:

7

= \frac{( 5 m + 25 ) ( m + 1 )}{2 ( 10 m + 50 )}

Factor

5 m + 25 : 5 (m + 5)

= \frac{5 ( m + 5 ) ( m + 1 )}{2 ( 10 m + 50 )}

Factor

10 m + 50 : 10 (m + 5)

= \frac{5 ( m + 5 ) ( m + 1 )}{2 \cdot 10 ( m + 5 )}

Cancel the common factor:

m + 5

= \frac{5 ( m + 1 )}{2 \cdot 10}

Factor the number:

10 = 5 \cdot 2

= \frac{5 ( m + 1 )}{2 \cdot 5 \cdot 2}

Cancel the common factor:

5

= \frac{m + 1}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{m + 1}{4}

(x^{4} - y)^{5}

(3 x + 2) (x^{2} - 4 x - 2)

x + \frac{1}{x}

3 \cdot 1

\frac{3}{x + 7} - \frac{7 x}{x ^{2} + 9 x + 14}

What is (5m+25)/(14)*(7m+7)/(10m+50) ?
The solution to (5m+25)/(14)*(7m+7)/(10m+50) is (m+1)/4