Question

Subtracting rational expressions: 6 - x+5/(7x-5)(x+4) Please show work

Answer 1

Answer:

$\dfrac{42x^2+137x-125}{7x^2+23x-20}$

Explanation:

You know that the sum of a number and a fraction is ...

... a + b/c = (ac +b)/c

Here, you have ...

... a = 6

... b = -(x+5)

... c = (7x-5)(x+4) = 7x² +23x -20

Then ...

... (ac +b)/c = (6(7x² +23x -20) -(x +5))/(7x² +23x -20)

... = (42x² +138x -120 -x -5)/(7x² +23x -20)

... = (42x² +137x -125)/(7x² +23x -20)