What is (2a-7)/a*(3a^2)/(2a^2-11a+14) ?

The solution to (2a-7)/a*(3a^2)/(2a^2-11a+14) is (3a)/(a-2)

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simplify (2a-7)/a*(3a^2)/(2a^2-11a+14)

simplify

\frac{2 a - 7}{a} \cdot \frac{3 a ^{2}}{2 a ^{2} - 11 a + 14}

\frac{3 a}{a - 2}

Solution steps

\frac{2 a - 7}{a} \cdot \frac{3 a ^{2}}{2 a ^{2} - 11 a + 14}

Apply the fraction rule:

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

= \frac{( 2 a - 7 ) \cdot 3 a ^{2}}{a ( 2 a ^{2} - 11 a + 14 )}

Apply exponent rule:

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

a^{2} = aa

= \frac{( 2 a - 7 ) \cdot 3 aa}{a ( 2 a ^{2} - 11 a + 14 )}

Cancel the common factor:

a

= \frac{( 2 a - 7 ) \cdot 3 a}{2 a ^{2} - 11 a + 14}

Factor

2 a^{2} - 11 a + 14 : (a - 2) (2 a - 7)

= \frac{( 2 a - 7 ) \cdot 3 a}{( a - 2 ) ( 2 a - 7 )}

Cancel the common factor:

2 a - 7

= \frac{3 a}{a - 2}

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\frac{2 π}{\frac{1}{8}}

\frac{6 x ^{2} y ^{3}}{( - 4 x ^{4} y ) ( - 3 x ^{3} y ^{2} )}

\frac{2 x - 3}{4} + 6 \geq 2 + \frac{4 x}{3}

What is (2a-7)/a*(3a^2)/(2a^2-11a+14) ?
The solution to (2a-7)/a*(3a^2)/(2a^2-11a+14) is (3a)/(a-2)