What is (x+2)/(x-4)+2/x+(5x)/(3x-1) ?

The solution to (x+2)/(x-4)+2/x+(5x)/(3x-1) is (8x^3-9x^2-28x+8)/(x(x-4)(3x-1))

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simplify (x+2)/(x-4)+2/x+(5x)/(3x-1)

simplify

\frac{x + 2}{x - 4} + \frac{2}{x} + \frac{5 x}{3 x - 1}

\frac{8 x ^{3} - 9 x ^{2} - 28 x + 8}{x ( x - 4 ) ( 3 x - 1 )}

Solution steps

\frac{x + 2}{x - 4} + \frac{2}{x} + \frac{5 x}{3 x - 1}

Least Common Multiplier of

x - 4, x, 3 x - 1 : x (x - 4) (3 x - 1)

Adjust Fractions based on the LCM

= \frac{( x + 2 ) x ( 3 x - 1 )}{x ( x - 4 ) ( 3 x - 1 )} + \frac{2 ( x - 4 ) ( 3 x - 1 )}{x ( x - 4 ) ( 3 x - 1 )} + \frac{5 x ^{2} ( x - 4 )}{x ( x - 4 ) ( 3 x - 1 )}

Apply the fraction rule:

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

= \frac{( x + 2 ) x ( 3 x - 1 ) + 2 ( x - 4 ) ( 3 x - 1 ) + 5 x ^{2} ( x - 4 )}{x ( x - 4 ) ( 3 x - 1 )}

Simplify

(x + 2) x (3 x - 1) + 2 (x - 4) (3 x - 1) + 5 x^{2} (x - 4) : 8 x^{3} - 9 x^{2} - 28 x + 8

= \frac{8 x ^{3} - 9 x ^{2} - 28 x + 8}{x ( x - 4 ) ( 3 x - 1 )}

\frac{x ^{2} + x}{x}

lo g_{x} (4)

\frac{22}{8}

\frac{22}{9}

(3 x^{2}) (- x^{3} y) (- a^{2} x)

What is (x+2)/(x-4)+2/x+(5x)/(3x-1) ?
The solution to (x+2)/(x-4)+2/x+(5x)/(3x-1) is (8x^3-9x^2-28x+8)/(x(x-4)(3x-1))