What is (x+2)/(3x)+(x^2-2)/(5x^2)+(2-x^3)/(9x^3) ?

The solution to (x+2)/(3x)+(x^2-2)/(5x^2)+(2-x^3)/(9x^3) is (19x^3+30x^2-18x+10)/(45x^3)

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simplify (x+2)/(3x)+(x^2-2)/(5x^2)+(2-x^3)/(9x^3)

simplify

\frac{x + 2}{3 x} + \frac{x ^{2} - 2}{5 x ^{2}} + \frac{2 - x ^{3}}{9 x ^{3}}

\frac{19 x ^{3} + 30 x ^{2} - 18 x + 10}{45 x ^{3}}

Solution steps

\frac{x + 2}{3 x} + \frac{x ^{2} - 2}{5 x ^{2}} + \frac{2 - x ^{3}}{9 x ^{3}}

Least Common Multiplier of

3 x, 5 x^{2}, 9 x^{3} : 45 x^{3}

Adjust Fractions based on the LCM

= \frac{( x + 2 ) \cdot 15 x ^{2}}{45 x ^{3}} + \frac{( x ^{2} - 2 ) \cdot 9 x}{45 x ^{3}} + \frac{( 2 - x ^{3} ) \cdot 5}{45 x ^{3}}

Apply the fraction rule:

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

= \frac{( x + 2 ) \cdot 15 x ^{2} + ( x ^{2} - 2 ) \cdot 9 x + ( 2 - x ^{3} ) \cdot 5}{45 x ^{3}}

Simplify

(x + 2) \cdot 15 x^{2} + (x^{2} - 2) \cdot 9 x + (2 - x^{3}) \cdot 5 : 19 x^{3} + 30 x^{2} - 18 x + 10

= \frac{19 x ^{3} + 30 x ^{2} - 18 x + 10}{45 x ^{3}}

1.5 \times 3

⌊ 0.5 ⌋

x - 4^{2}

\frac{15 q}{( 3 q ^{3} ) ^{2}}

\frac{x ^{2} + 4 x + 3}{x ^{2} - x - 2}

What is (x+2)/(3x)+(x^2-2)/(5x^2)+(2-x^3)/(9x^3) ?
The solution to (x+2)/(3x)+(x^2-2)/(5x^2)+(2-x^3)/(9x^3) is (19x^3+30x^2-18x+10)/(45x^3)