What is (6m^2+7m-5)/(10m^2-5m)*(10m^2)/(9m^2-25) ?

The solution to (6m^2+7m-5)/(10m^2-5m)*(10m^2)/(9m^2-25) is (2m)/(3m-5)

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simplify (6m^2+7m-5)/(10m^2-5m)*(10m^2)/(9m^2-25)

simplify

\frac{6 m ^{2} + 7 m - 5}{10 m ^{2} - 5 m} \cdot \frac{10 m ^{2}}{9 m ^{2} - 25}

\frac{2 m}{3 m - 5}

Solution steps

\frac{6 m ^{2} + 7 m - 5}{10 m ^{2} - 5 m} \cdot \frac{10 m ^{2}}{9 m ^{2} - 25}

Cancel

\frac{6 m ^{2} + 7 m - 5}{10 m ^{2} - 5 m} : \frac{3 m + 5}{5 m}

= \frac{3 m + 5}{5 m} \cdot \frac{10 m ^{2}}{9 m ^{2} - 25}

Apply the fraction rule:

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

= \frac{( 3 m + 5 ) \cdot 10 m ^{2}}{5 m ( 9 m ^{2} - 25 )}

Factor the number:

10 = 5 \cdot 2

= \frac{( 3 m + 5 ) \cdot 5 \cdot 2 m ^{2}}{5 m ( 9 m ^{2} - 25 )}

Cancel the common factor:

5

= \frac{( 3 m + 5 ) \cdot 2 m ^{2}}{m ( 9 m ^{2} - 25 )}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

m^{2} = mm

= \frac{( 3 m + 5 ) \cdot 2 mm}{m ( 9 m ^{2} - 25 )}

Cancel the common factor:

m

= \frac{( 3 m + 5 ) \cdot 2 m}{9 m ^{2} - 25}

Factor

9 m^{2} - 25 : (3 m + 5) (3 m - 5)

= \frac{( 3 m + 5 ) \cdot 2 m}{( 3 m + 5 ) ( 3 m - 5 )}

Cancel the common factor:

3 m + 5

= \frac{2 m}{3 m - 5}

20 x^{2} + 27 x + 9

\frac{1}{x - 2} \geq \frac{3}{x + 1}

6 x - 8 = 8 x - 6

6 - 2 x = 3

lo g_{6} (1)

What is (6m^2+7m-5)/(10m^2-5m)*(10m^2)/(9m^2-25) ?
The solution to (6m^2+7m-5)/(10m^2-5m)*(10m^2)/(9m^2-25) is (2m)/(3m-5)