What is 6/(7k^5+23k^4+6k^3)-(k^2)/(2k+6) ?

The solution to 6/(7k^5+23k^4+6k^3)-(k^2)/(2k+6) is (12-7k^6-2k^5)/(2k^3(k+3)(7k+2))

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simplify 6/(7k^5+23k^4+6k^3)-(k^2)/(2k+6)

simplify

\frac{6}{7 k ^{5} + 23 k ^{4} + 6 k ^{3}} - \frac{k ^{2}}{2 k + 6}

\frac{12 - 7 k ^{6} - 2 k ^{5}}{2 k ^{3} ( k + 3 ) ( 7 k + 2 )}

Solution steps

\frac{6}{7 k ^{5} + 23 k ^{4} + 6 k ^{3}} - \frac{k ^{2}}{2 k + 6}

Least Common Multiplier of

7 k^{5} + 23 k^{4} + 6 k^{3}, 2 k + 6 : 2 k^{3} (k + 3) (7 k + 2)

Adjust Fractions based on the LCM

= \frac{12}{2 k ^{3} ( k + 3 ) ( 7 k + 2 )} - \frac{k ^{5} ( 7 k + 2 )}{2 k ^{3} ( k + 3 ) ( 7 k + 2 )}

Apply the fraction rule:

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

= \frac{12 - k ^{5} ( 7 k + 2 )}{2 k ^{3} ( k + 3 ) ( 7 k + 2 )}

Simplify

12 - k^{5} (7 k + 2) : 12 - 7 k^{6} - 2 k^{5}

= \frac{12 - 7 k ^{6} - 2 k ^{5}}{2 k ^{3} ( k + 3 ) ( 7 k + 2 )}

3^{2} + (- 1)^{2}

- \frac{4}{3} x = 14

7 x + 1 < 4 (x - 2)

x^{3} + 5 x^{2} + 8 x

What is 6/(7k^5+23k^4+6k^3)-(k^2)/(2k+6) ?
The solution to 6/(7k^5+23k^4+6k^3)-(k^2)/(2k+6) is (12-7k^6-2k^5)/(2k^3(k+3)(7k+2))