perform the indicated operation?

Question

1.) (x^2)/(x-3) - (9)/ (x-3)


2.) (x)/ (x+2) -(3/4)

Answer 1

1. x^2/(x-3) - 9/(x-3)

*Denominators match - combine the numerators.

==> (x^2-9)/(x-3)

First: factor the numerator (Difference of Squares).

==> [(x+3)(x-3)]/(x-3)

Sec: cross cancel the same terms....

==> x+3

2. x/(x+2) - 3/4

*Denominators need to match - find the greatest common denominator, which is 4(x+2).

First: multiply both denominators & their corresponding numerators with the missing terms to get the greatest common denominator.

==> 4[x/(x+2)] - (x+2)(3/4)
==> 4x/[4(x+2)] - [3(x+2)/4(x+2)]
==> 4x/[4(x+2)] - [(3x+6)/4(x+2)]

Sec: combine the numerators....

==> [4x-(3x+6)]/4(x+2)
==> [4x-3x-6]/4(x+2)
==> x-6/4(x+2)

Answer 2

1. (x^2 - 9)/(x-3)
=(x+3)(x-3)/(x-3)
= x + 3

(4x-3(x+2))/(4(x+2))
=(x-6)/4(x+2)

Answer 3

(x^2-9)/(x-3)=(x+3)(x-3)/(x-3)=x+3


common denominator
(4x-3(x+2))/(x+2)4=(4x-3x-2)/4(x+2)=(x-2)/4(x+2)

Answer 4

1) since both terms are over the same denominator, you can put both numerators in the same term

A/C - B/C = (A-B)/C

Once you do that, the numerator becomes a difference of squares, of the form:

x^2 - a^2 = (x+a)(x-a)

Once you have written it in that form,
(x+a)(x-a) / C

then you check if anything simplifies