What is (3k^2-84k+588)/(784-4k^2) ?

The solution to (3k^2-84k+588)/(784-4k^2) is -(3(k-14))/(4(14+k))

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simplify (3k^2-84k+588)/(784-4k^2)

simplify

\frac{3 k ^{2} - 84 k + 588}{784 - 4 k ^{2}}

- \frac{3 ( k - 14 )}{4 ( 14 + k )}

Solution steps

\frac{3 k ^{2} - 84 k + 588}{784 - 4 k ^{2}}

Factor

3 k^{2} - 84 k + 588 : 3 (k - 14)^{2}

= \frac{3 ( k - 14 ) ^{2}}{784 - 4 k ^{2}}

Factor

784 - 4 k^{2} : 4 (14 + k) (14 - k)

= \frac{3 ( k - 14 ) ^{2}}{4 ( 14 + k ) ( 14 - k )}

4 (14 + k) (14 - k) = - 4 (14 + k) (k - 14)

= \frac{3 ( k - 14 ) ^{2}}{- 4 ( 14 + k ) ( k - 14 )}

Apply exponent rule:

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

(k - 14)^{2} = (k - 14) (k - 14)

= \frac{3 ( k - 14 ) ( k - 14 )}{- 4 ( 14 + k ) ( k - 14 )}

Cancel the common factor:

k - 14

= \frac{3 ( k - 14 )}{- 4 ( 14 + k )}

Apply the fraction rule:

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

= - \frac{3 ( k - 14 )}{4 ( 14 + k )}

\frac{3 x}{4} - \frac{x - 1}{5} = 0

2 x - 4 < 10 or - 2 x + 1 \geq - 11

36 x^{2} - 204 x + 289

8 - 3 (4 x - 1) \leq - 49

\frac{4}{3} \cdot \frac{5}{3}

What is (3k^2-84k+588)/(784-4k^2) ?
The solution to (3k^2-84k+588)/(784-4k^2) is -(3(k-14))/(4(14+k))