Equation at the end of step 1 :
(2x - 6) x
—————————— - —————
((x2) - 9) x + 3
Step 2 :
2x - 6
Simplify ——————
x2 - 9
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
2x - 6 = 2 • (x - 3)
Trying to factor as a Difference of Squares :
3.2 Factoring: x2 - 9
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 9 is the square of 3
Check : x2 is the square of x1
Factorization is : (x + 3) • (x - 3)
Canceling Out :
3.3 Cancel out (x - 3) which appears on both sides of the fraction line.
Equation at the end of step 3 :
2 x
————— - —————
x + 3 x + 3
Step 4 :
Adding fractions which have a common denominator :
4.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2 - (x) 2 - x
——————— = —————
x+3 x + 3
Final result :
2 - x
—————
x + 3
