2nd request for help adding 2 algebraic fractions.?

Question

( x + 1) ( 4x - 3 )
______ + _______
- ( x - 5) ( x - 5 )

They don't line exactly right, but please help.

Answer 1

first, simplify the denominator by multiplying the first term by -1

you'll get
[(-x - 1) / (x - 5)] + [(4x - 3) / (x - 5)]

then combine the terms to get
(-x - 1 + 4x - 3) / (x - 5)
and reduce to get
(3x - 4) / (x - 5)

Answer 2

You need to get similar denominators.

One thing. a / -b = -a / b

So the first fraction can be rewritten as - (x + 1) / (x -5)

That gives you the same denominator on both sides.

(- (x + 1) + (4x - 3)) / (x - 5)
(-x - 1 + 4x - 3) / (x - 5)
(3x - 4) / (x - 5)