Question

Can an expert solve this math question for me? Please show steps so I can understand... I would really appreciate it.

1/2x^2+4x + 1/x^3+2x^2 =

Answer 1

`(1)/(2x^2)`

Explanation:

When you add fractions, the fractions must have common denominators.

Multiply the denominators together to get a common denominator.

(2
`x^(2)`+4x) by (
`x^3`+2
`x^(2)`) =
`2x^5+8x^4+8x^3`

This is the common denominator.

However, you also need to multiply the numerators.

For example,

`(1)/(2) + (1)/(4)`

2 times 4 is 8.

But 1/8 + 1/8 isn't the answer. Thats 2/8 or 1/4.

If you multiply 1 by 4 and 2 by 1, however, you'll get the correct answer.

Multiply 1 by x^3 + 2x^2 and 1 by 2x^2 + 4x.

This results in:

`(x^3+2x^2)/(2x^5+8x^4+8x^3) +(2x^2+4x)/(2x^5+8x^4+8x^3)`

Since they have a common denominator, you can just put the numbers over one denominator like:

`(x^3+2x^2+2x^2+4x)/(2x^5+8x^4+8x^3)`

Both the and numerators can be factored.

The numerator can be factored into x
`(x+2)^2`.

The denominator can be factored into
`2x^3(x+2)^2`

Like:

`(x(x+2)^2)/(2x^3(x+2)^2)`

The (x+2)^2 cancel, leaving:

`(x)/(2x^3)`

Which is basically:
`(x^1)/(2x^3)`

Which simplifies to

`(1)/(2x^2)`

Like this?:

`(1)/(2x^2+4x) + (1)/(x^3+2x^2)`