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How do you combine #(x+2)/(5x^2)+(x+4)/(15x)#?

Answer 1

Julia Adams

#[x^2 + 7x+ 6]/(15x^2)#

Adding fractions requires a common denominator.

The LCD is #15x^2#

An equivalent fraction for each fraction must be found with the denominator #15x^2#

#color(magenta)[(x+2)/(5x^2])+color(blue)[(x+4)/(15x)]#

#color(magenta)[(x+2)/(5x^2) xx 3/3 = (3(x+2))/(15x^2])#

#color(blue)[(x+4)/(15x) xx x/x = (x(x+4))/(15x^2)]# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(magenta)[(x+2)/(5x^2])+color(blue)[(x+4)/(15x)]#

=#color(magenta)[(3(x+2))/(15x^2)] + color(blue)[(x(x+4))/(15x^2) ]#

= #[color(magenta)(3x+6) + color(blue)(x^2+4x])/(15x^2)#

= #[x^2 + 7x+ 6]/(15x^2)#

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Answer 2

Abigail Allen

To combine the expressions (x+2)/(5x^2) and (x+4)/(15x), we need to find a common denominator. The common denominator for these two expressions is 15x^2.

To do this, we multiply the first expression by (3x)/(3x) and the second expression by (x^2)/(x^2).

After simplifying, we get (3x^2 + 6x + x^3 + 4x^2)/(15x^2).

Combining like terms, the final expression is (x^3 + 7x^2 + 6x)/(15x^2).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.