how do i solve (2x+5)/(x^2-3x-10) + (x+1)/(x+2)

Question

muzzack · Answer

x • (x - 2)   
  —————————————————
       (x + 2) • (x - 5)

muzzack · Answer

want me to do it step by stpe

solomonzelman · Answer

Hint,        $\normalsize\color{blue}{ \rm   x^2-3x-10=(x+2)(x-5)  }$    now, find the common denominator.

anonymous · Answer

$$\frac{ 2x+5 }{ x ^{2}-3x-10 } + \frac{ x+1 }{ x+2 }$$

anonymous · Answer

yes please @Muzzack

muzzack · Answer

Step  1:
 You will have to simplify 
$$\frac{2x + 5 }{ x^2 - 3x - 10 }   $$

muzzack · Answer

then you get        (2x + 5)                                    (x + 1)
              ————————————————— +  ———————
                     (x + 2) • (x - 5)                                 x + 2

anonymous · Answer

ok then what?

muzzack · Answer

Step  2  :

                                 2x+5                 x+1 
Simplify   ———————————  +  —————
                      (x+2)•(x-5)                    (x+2)

muzzack · Answer

Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 (2x+5) + (x+1) • (x-5)                                               x^2 - 2x     
 ——————————————————————  =  —————————————————
     (x+2) • (x-5)                                                          (x + 2) • (x - 5)

Pull out like factors :

   x^2 - 2x  =   x • (x - 2) 
Final result :

     x • (x - 2)   
  —————————————————
  (x + 2) • (x - 5)

anonymous · Answer

oh my gosh thanks I get it now!

muzzack · Answer

ur welcome