Step by Step Solution
Step 1 :
3r - 3
Simplify ——————
r2
Step 2 :
Pulling out like terms :
2.1 Pull out like factors :
3r - 3 = 3 • (r - 1)
Equation at the end of step 2 :
r 3•(r-1) (15•———————————————————)•——————— (((18•(r2))+9r)-27) r2Step 3 :
Equation at the end of step 3 :
r 3•(r-1)
(15•——————————————————)•———————
(((2•32r2)+9r)-27) r2
Step 4 :
r
Simplify ——————————————
18r2 + 9r - 27
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
18r2 + 9r - 27 = 9 • (2r2 + r - 3)
Trying to factor by splitting the middle term
5.2 Factoring 2r2 + r - 3
The first term is, 2r2 its coefficient is 2 .
The middle term is, +r its coefficient is 1 .
The last term, "the constant", is -3
Step-1 : Multiply the coefficient of the first term by the constant 2 • -3 = -6
Step-2 : Find two factors of -6 whose sum equals the coefficient of the middle term, which is 1 .
| -6 | + | 1 | = | -5 | ||
| -3 | + | 2 | = | -1 | ||
| -2 | + | 3 | = | 1 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 3
2r2 - 2r + 3r - 3
Step-4 : Add up the first 2 terms, pulling out like factors :
2r • (r-1)
Add up the last 2 terms, pulling out common factors :
3 • (r-1)
Step-5 : Add up the four terms of step 4 :
(2r+3) • (r-1)
Which is the desired factorization
Equation at the end of step 5 :
r 3•(r-1)
(15•——————————————)•———————
9•(r-1)•(2r+3) r2
Step 6 :
Equation at the end of step 6 :
5r 3 • (r - 1)
—————————————————————— • ———————————
3 • (r - 1) • (2r + 3) r2
Step 7 :
Canceling Out :
7.1 Cancel out (r-1) which appears on both sides of the fraction line.
Dividing exponential expressions :
7.2 r1 divided by r2 = r(1 - 2) = r(-1) = 1/r1 = 1/r
Final result :
5
————————————
r • (2r + 3)
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