((8p3+16p2)/(20p+40))/((2p-10)/(2p2-12p+10)) Final result : 2p2 • (p - 1)
—————————————
5
Step by step solution :
Step 1 :Skip Ad
Equation at the end of step 1 : ((8•(p3))+(16•(p2))) (2p-10)
———————————————————— ÷ ——————————————
(20p+40) ((2p2-12p)+10)
Step 2 : 2p - 10
Simplify ——————————————
2p2 - 12p + 10
Step 3 :Pulling out like terms :
3.1 Pull out like factors :
2p - 10 = 2 • (p - 5)
Step 4 :Pulling out like terms :
4.1 Pull out like factors :
2p2 - 12p + 10 = 2 • (p2 - 6p + 5)
Trying to factor by splitting the middle term
4.2 Factoring p2 - 6p + 5
The first term is, p2 its coefficient is 1 .
The middle term is, -6p its coefficient is -6 .
The last term, "the constant", is +5
Step-1 : Multiply the coefficient of the first term by the constant 1 • 5 = 5
Step-2 : Find two factors of 5 whose sum equals the coefficient of the middle term, which is -6 .
-5 + -1 = -6 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and -1
p2 - 5p - 1p - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
p • (p-5)
Add up the last 2 terms, pulling out common factors :
1 • (p-5)
Step-5 : Add up the four terms of step 4 :
(p-1) • (p-5)
Which is the desired factorization
Canceling Out :
4.3 Cancel out (p-5) which appears on both sides of the fraction line.
Equation at the end of step 4 : ((8•(p3))+(16•(p2))) 1
———————————————————— ÷ ———
(20p+40) p-1
Step 5 :Equation at the end of step 5 : ((8•(p3))+24p2) 1
——————————————— ÷ ———
(20p+40) p-1
Step 6 :Equation at the end of step 6 : (23p3 + 24p2) 1
————————————— ÷ —————
(20p + 40) p - 1
Step 7 : 8p3 + 16p2
Simplify ——————————
20p + 40
Step 8 :Pulling out like terms :
8.1 Pull out like factors :
8p3 + 16p2 = 8p2 • (p + 2)
Step 9 :Pulling out like terms :
9.1 Pull out like factors :
20p + 40 = 20 • (p + 2)
Canceling Out :
9.2 Cancel out (p + 2) which appears on both sides of the fraction line.
Equation at the end of step 9 : 2p2 1
——— ÷ —————
5 p - 1
Step 10 : 2p2 1
Divide ——— by —————
5 (p-1)
10.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
2p2 1 2p2 p - 1
——— ÷ ——————— = ——— • —————
5 (p - 1) 5 1
Final result :
2p2 • (p - 1)
—————————————
5
