Question

What is the simplified form of the quantity of x plus 8, all over the quantity of x plus 2 + the quantity of x minus 3, all over 4?

Answer 1

`(x + 8)/(x + 2) + (x - 3)/(4) = (4(x + 8))/(4(x + 2)) + ((x + 2)(x - 3))/(4(x + 2)) = (4(x) + 4(8))/(4(x + 2)) + (x(x - 3) + 2(x - 3))/(4(x + 2)) = (4x + 32)/(4(x + 2)) + (x(x) - x(3) + 2(x) - 2(3))/(4(x + 2)) = (4x + 32)/(4(x + 2)) + (x^(2) - 3x + 2x - 6)/(4(x + 2)) = (4x + 32)/(4(x + 2)) + (x^(2) - x - 6)/(4(x + 2)) = ((4x + 32) + (x^(2) - x - 6)/(4(x + 2)) = (x^(2) + (4x - x) + (32 - 6))/(4(x + 2)) = (x^(2) + 3x + 26)/(4(x + 2))`

Answer 2

Answer:
`(x^2+3x+26)/(4x+8)`

Explanation:

Since, according to the question the given expression,

`(x+8)/(x+2) + (x-3)/(4)`

=
`(4(x+8)+(x-3)(x+2))/(4(x+2))`

=
`(4x+32+(x-3)(x+2))/(4x+8)` (By solving the parenthesis )

=
`(4x+32+x(x+2)-3(x+2))/(4x+8)` ( by distributive property)

=
`(4x+32+x^2+2x-3x-6)/(4x+8)` ( again on applying distributive property)

=
`(3x+26+x^2)/(4x+8)` ( by operating like terms)

=
`(x^2+3x+26)/(4x+8)`