Question

What is the simplified form of the quantity of x plus 7, all over the quantity of x plus 3 + the quantity of x minus 4, all over 3?

Answer 1

`(x^2+2x+9)/(3x+9)`

with the work being


`(x+7)/(x+3) + (x-4)/(3)`

multiply the left term by 3/3 and the right by (x+3)/(x+3), so it looks like
`(3(x+7))/(3(x+3)) + ((x+3)(x-4))/((x+3)3)`

then you can multiply out the tops of the fractions and add together, and you have a common denominator


`(3x+21)/(3x+9) + (x^2+3x-4x-12)/(3x+9) = (x^2+2x+9)/(3x+9)`