Answer:
STEP
1
:
10xy
Simplify ———————
8y + 3x
Equation at the end of step
1
:
10xy
((2 • (x + y)) • (8x + 24y)) + ———————
3x + 8y
STEP
2
:
Equation at the end of step 2
10xy
(2 • (x + y) • (8x + 24y)) + ———————
3x + 8y
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
8x + 24y = 8 • (x + 3y)
Equation at the end of step
4
:
10xy
16 • (x + y) • (x + 3y) + ———————
3x + 8y
STEP
5
:
Rewriting the whole as an Equivalent Fraction
5.1 Adding a fraction to a whole
Rewrite the whole as a fraction using (3x+8y) as the denominator :
16 • (x + y) • (x + 3y) 16 • (x + y) • (x + 3y) • (3x + 8y)
16 • (x + y) • (x + 3y) = ——————————————————————— = ———————————————————————————————————
1 (3x + 8y)
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 :
5.2 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:
16 • (x+y) • (x+3y) • (3x+8y) + 10xy 48x3 + 320x2y + 656xy2 + 10xy + 384y3
———————————————————————————————————— = —————————————————————————————————————
1 • (3x+8y) 1 • (3x + 8y)
STEP
6
:
Pulling out like terms :
6.1 Pull out like factors :
48x3 + 320x2y + 656xy2 + 10xy + 384y3 =
2 • (24x3 + 160x2y + 328xy2 + 5xy + 192y3)
Final result :
2 • (24x3 + 160x2y + 328xy2 + 5xy + 192y3)
——————————————————————————————————————————
3x + 8y
Step-by-step explanation:
Hope it helps :)
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