Answer:
Step-by-step explanation:
STEP
1
:
x
Simplify —
x
Equation at the end of step
1
:
(3•(x2))
————————+((6•1)-8)
(x-8)
STEP
2
:
Equation at the end of step
2
:
3x2
——————— + -2
(x - 8)
STEP
3
:
3x2
Simplify —————
x - 8
Equation at the end of step
3
:
3x2
————— + -2
x - 8
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Adding a whole to a fraction
Rewrite the whole as a fraction using (x-8) as the denominator :
-2 -2 • (x - 8)
-2 = —— = ————————————
1 (x - 8)
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Adding fractions that have a common denominator :
4.2 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:
3x2 + -2 • (x-8) 3x2 - 2x + 16
———————————————— = —————————————
1 • (x-8) 1 • (x - 8)
Trying to factor by splitting the middle term
4.3 Factoring 3x2 - 2x + 16
The first term is, 3x2 its coefficient is 3 .
The middle term is, -2x its coefficient is -2 .
The last term, "the constant", is +16
Step-1 : Multiply the coefficient of the first term by the constant 3 • 16 = 48
Step-2 : Find two factors of 48 whose sum equals the coefficient of the middle term, which is -2 .
-48 + -1 = -49
-24 + -2 = -26
-16 + -3 = -19
-12 + -4 = -16
-8 + -6 = -14
-6 + -8 = -14
