Solution - Simplification or other simple results

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x2"   was replaced by   "x^2".  1 more similar replacement(s).

Step  1  :

            x2 - 7x + 10
 Simplify   ————————————
            x2 - 2x - 15

Trying to factor by splitting the middle term

 1.1     Factoring  x² - 7x + 10 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -7x  its coefficient is  -7 .
The last term, "the constant", is  +10 

Step-1 : Multiply the coefficient of the first term by the constant   1 • 10 = 10 

Step-2 : Find two factors of  10  whose sum equals the coefficient of the middle term, which is   -7 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  -2 
                     x² - 5x - 2x - 10

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-5)
              Add up the last 2 terms, pulling out common factors :
                    2 • (x-5)
Step-5 : Add up the four terms of step 4 :
                    (x-2)  •  (x-5)
             Which is the desired factorization

Trying to factor by splitting the middle term

 1.2     Factoring  x²-2x-15 

The first term is,  x²  its coefficient is  1 .
The middle term is,  -2x  its coefficient is  -2 .
The last term, "the constant", is  -15 

Step-1 : Multiply the coefficient of the first term by the constant   1 • -15 = -15 

Step-2 : Find two factors of  -15  whose sum equals the coefficient of the middle term, which is   -2 .

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  3 
                     x² - 5x + 3x - 15

Step-4 : Add up the first 2 terms, pulling out like factors :
                    x • (x-5)
              Add up the last 2 terms, pulling out common factors :
                    3 • (x-5)
Step-5 : Add up the four terms of step 4 :
                    (x+3)  •  (x-5)
             Which is the desired factorization

Canceling Out :

 1.3    Cancel out  (x-5)  which appears on both sides of the fraction line.

Final result :

  x - 2
  —————
  x + 3