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Sagot :
Answer:
x-8/x-6
Step-by-step explanation:
Step by Step Solution
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STEP
1
:
8x - 32
Simplify —————————————
x2 - 10x + 24
STEP
2
:
Pulling out like terms
2.1 Pull out like factors :
8x - 32 = 8 • (x - 4)
Trying to factor by splitting the middle term
2.2 Factoring x2 - 10x + 24
The first term is, x2 its coefficient is 1 .
The middle term is, -10x its coefficient is -10 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 1 • 24 = 24
Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is -10 .
-24 + -1 = -25
-12 + -2 = -14
-8 + -3 = -11
-6 + -4 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -4
x2 - 6x - 4x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
4 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x-4) • (x-6)
Which is the desired factorization
Canceling Out :
2.3 Cancel out (x-4) which appears on both sides of the fraction line.
Equation at the end of step
2
:
((x2)-4x) 8
———————————————-———
(((x2)-10x)+24) x-6
STEP
3
:
x2 - 4x
Simplify —————————————
x2 - 10x + 24
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
x2 - 4x = x • (x - 4)
Trying to factor by splitting the middle term
4.2 Factoring x2 - 10x + 24
The first term is, x2 its coefficient is 1 .
The middle term is, -10x its coefficient is -10 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 1 • 24 = 24
Step-2 : Find two factors of 24 whose sum equals the coefficient of the middle term, which is -10 .
-24 + -1 = -25
-12 + -2 = -14
-8 + -3 = -11
-6 + -4 = -10 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -6 and -4
x2 - 6x - 4x - 24
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-6)
Add up the last 2 terms, pulling out common factors :
4 • (x-6)
Step-5 : Add up the four terms of step 4 :
(x-4) • (x-6)
Which is the desired factorization
Canceling Out :
4.3 Cancel out (x-4) which appears on both sides of the fraction line.
Equation at the end of step
4
:
x 8
————— - —————
x - 6 x - 6
STEP
5
:
Adding fractions which have a common denominator :
5.1 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:
x - (8) x - 8
——————— = —————
x-6 x - 6
Final result :
x - 8
—————
x - 6
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