What is (1-x)/(2x)+(x+2)/(x^2)+1/(3ax^2) ?

The solution to (1-x)/(2x)+(x+2)/(x^2)+1/(3ax^2) is (9ax-3ax^2+12a+2)/(6ax^2)

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simplify (1-x)/(2x)+(x+2)/(x^2)+1/(3ax^2)

simplify

\frac{1 - x}{2 x} + \frac{x + 2}{x ^{2}} + \frac{1}{3 a x ^{2}}

\frac{9 a x - 3 a x ^{2} + 12 a + 2}{6 a x ^{2}}

Solution steps

\frac{1 - x}{2 x} + \frac{x + 2}{x ^{2}} + \frac{1}{3 a x ^{2}}

Least Common Multiplier of

2 x, x^{2}, 3 a x^{2} : 6 a x^{2}

Adjust Fractions based on the LCM

= \frac{( 1 - x ) \cdot 3 a x}{6 a x ^{2}} + \frac{( x + 2 ) \cdot 6 a}{6 a x ^{2}} + \frac{2}{6 a x ^{2}}

Apply the fraction rule:

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

= \frac{( 1 - x ) \cdot 3 a x + ( x + 2 ) \cdot 6 a + 2}{6 a x ^{2}}

Simplify

(1 - x) \cdot 3 a x + (x + 2) \cdot 6 a + 2 : 9 a x - 3 a x^{2} + 12 a + 2

= \frac{9 a x - 3 a x ^{2} + 12 a + 2}{6 a x ^{2}}

\frac{3 x}{3}

(7 x - 1)^{2}

lo g_{\frac{1}{2}} (\frac{1}{8})

lo g_{5} (15)

\frac{x ^{2} - 3 x}{x ^{2} + 3 x}

What is (1-x)/(2x)+(x+2)/(x^2)+1/(3ax^2) ?
The solution to (1-x)/(2x)+(x+2)/(x^2)+1/(3ax^2) is (9ax-3ax^2+12a+2)/(6ax^2)