Question

How do you simplify `(6g)/(g+5)-(g-2)/(2g)`?

Answer 1

`(11g^2-3g+10)/(2g(g+5))`

Explanation:

Before we can subtract the fractions we require them to have a
`color(blue)"common denominator"`

This is achieved by multiplying the numerator/denominator of

`(6g)/(g+5)" by 2g and the numerator/denominator of " (g-2)/(2g)`

by (g + 5)

`rArr((6g)/(g+5)xx(2g)/(2g))-((g-2)/(2g)xx(g+5)/(g+5))`

`=(12g^2)/(2g(g+5))-((g-2)(g+5))/(2g(g+5))`

Now that the fractions have a common denominator we can subtract the numerators, leaving the denominator as it is.

`=(12g^2-(g^2+3g-10))/(2g(g+5))`

`=(12g^2-g^2-3g+10)/(2g(g+5))`

`=(11g^2-3g+10)/(2g(g+5))`