Respuesta :
Answer:
[tex]\frac{1}{2x^2}[/tex]
Step-by-step explanation:
When you add fractions, the fractions must have common denominators.
Multiply the denominators together to get a common denominator.
(2[tex]x^{2}[/tex]+4x) by ([tex]x^3[/tex]+2[tex]x^{2}[/tex]) = [tex]2x^5+8x^4+8x^3[/tex]
This is the common denominator.
However, you also need to multiply the numerators.
For example,
[tex]\frac{1}{2} + \frac{1}{4}[/tex]
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:
[tex]\frac{x^3+2x^2}{2x^5+8x^4+8x^3} +\frac{2x^2+4x}{2x^5+8x^4+8x^3}[/tex]
Since they have a common denominator, you can just put the numbers over one denominator like:
[tex]\frac{x^3+2x^2+2x^2+4x}{2x^5+8x^4+8x^3}[/tex]
Both the and numerators can be factored.
The numerator can be factored into x[tex](x+2)^2[/tex].
The denominator can be factored into [tex]2x^3(x+2)^2[/tex]
Like:
[tex]\frac{x(x+2)^2}{2x^3(x+2)^2}[/tex]
The (x+2)^2 cancel, leaving:
[tex]\frac{x}{2x^3}[/tex]
Which is basically: [tex]\frac{x^1}{2x^3}[/tex]
Which simplifies to
[tex]\frac{1}{2x^2}[/tex]
Like this?:
[tex]\frac{1}{2x^2+4x} + \frac{1}{x^3+2x^2}[/tex]
