Question

Simplify the expression completely.

Answer 1

\[\frac{ 2 }{ x }-\frac{ 5x-4 }{ x ^{2} }+\frac{ x+3 }{ x ^{3}}\]

Answer 2

To get rid of the denominators, multiply both sides by the LCD.

Answer 3

I did that. I got the answer \[-\frac{ 3(x ^{2} -x+1)}{ x ^{3} }\] But it says it s not right

Answer 4

Ok. I just looked at this problem more carefully.
This is not an equation, so there are no "two sides."

What you need to do is to add and subtract fractions, so you need a common denominator.
The LCD of x, x^2, and x^3 is x^3.

\(\large \dfrac{ 2 }{ x }-\dfrac{ 5x-4 }{ x ^{2} }+\dfrac{ x+3 }{ x ^{3}}\)

\(\large =\dfrac{x^2}{x^2}\cdot\dfrac{ 2 }{ x }-\dfrac{x}{x} \cdot \dfrac{ 5x-4 }{ x ^{2} }+\dfrac{ x+3 }{ x ^{3}}\)

\(\large =\dfrac{2x^2}{x^3}- \dfrac{ 5x^2-4x }{ x ^3 }+\dfrac{ x+3 }{ x ^{3}}\)

Ok so far?

Answer 5

yes

Answer 6

\(\large =\dfrac{2x^2 - 5x^2+4x +x+3 }{ x ^{3}}\)

\(\large =\dfrac{-3x^2+5x+3 }{ x ^{3}}\)

Answer 7

how did the minus sign between the 5 and 4 turn +

Answer 8

Good question.
It's because the - before the fraction is as if it is a -1 that has to be multiplied by every term in the numerator of the fraction.