What is (5a^2+19a-4)/(1-25a^2) ?

The solution to (5a^2+19a-4)/(1-25a^2) is -(a+4)/(1+5a)

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simplify (5a^2+19a-4)/(1-25a^2)

simplify

\frac{5 a ^{2} + 19 a - 4}{1 - 25 a ^{2}}

- \frac{a + 4}{1 + 5 a}

Solution steps

\frac{5 a ^{2} + 19 a - 4}{1 - 25 a ^{2}}

Factor

5 a^{2} + 19 a - 4 : (5 a - 1) (a + 4)

= \frac{( 5 a - 1 ) ( a + 4 )}{1 - 25 a ^{2}}

Factor

1 - 25 a^{2} : (1 + 5 a) (1 - 5 a)

= \frac{( 5 a - 1 ) ( a + 4 )}{( 1 + 5 a ) ( 1 - 5 a )}

(1 + 5 a) (1 - 5 a) = - (1 + 5 a) (5 a - 1)

= \frac{( 5 a - 1 ) ( a + 4 )}{- ( 1 + 5 a ) ( 5 a - 1 )}

Cancel the common factor:

5 a - 1

= \frac{a + 4}{- ( 1 + 5 a )}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{a + 4}{1 + 5 a}

\frac{8}{20} - \frac{1}{4}

\frac{1}{5} \div \frac{2}{7}

\frac{3}{2} - \frac{7}{5}

12 \times 12

+ \frac{5}{6} \cdot + \frac{1}{4}

What is (5a^2+19a-4)/(1-25a^2) ?
The solution to (5a^2+19a-4)/(1-25a^2) is -(a+4)/(1+5a)