Solution - Simplification or other simple results
Other Ways to Solve
Simplification or other simple resultsStep by Step Solution
Step 1 :
Equation at the end of step 1 :
(((2•(x2))-x)-6) (((x2)-x)-20)
———————————————— ÷ —————————————
((x2)+3x) ((2x2-7x)-15)
Step 2 :
x2 - x - 20
Simplify —————————————
2x2 - 7x - 15
Trying to factor by splitting the middle term
2.1 Factoring x2 - x - 20
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -20
Step-1 : Multiply the coefficient of the first term by the constant 1 • -20 = -20
Step-2 : Find two factors of -20 whose sum equals the coefficient of the middle term, which is -1 .
| -20 | + | 1 | = | -19 | ||
| -10 | + | 2 | = | -8 | ||
| -5 | + | 4 | = | -1 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 4
x2 - 5x + 4x - 20
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (x-5)
Add up the last 2 terms, pulling out common factors :
4 • (x-5)
Step-5 : Add up the four terms of step 4 :
(x+4) • (x-5)
Which is the desired factorization
Trying to factor by splitting the middle term
2.2 Factoring 2x2-7x-15
The first term is, 2x2 its coefficient is 2 .
The middle term is, -7x its coefficient is -7 .
The last term, "the constant", is -15
Step-1 : Multiply the coefficient of the first term by the constant 2 • -15 = -30
Step-2 : Find two factors of -30 whose sum equals the coefficient of the middle term, which is -7 .
| -30 | + | 1 | = | -29 | ||
| -15 | + | 2 | = | -13 | ||
| -10 | + | 3 | = | -7 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and 3
2x2 - 10x + 3x - 15
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-5)
Add up the last 2 terms, pulling out common factors :
3 • (x-5)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (x-5)
Which is the desired factorization
Canceling Out :
2.3 Cancel out (x-5) which appears on both sides of the fraction line.
Equation at the end of step 2 :
(((2•(x2))-x)-6) (x+4) ———————————————— ÷ ————— ((x2)+3x) 2x+3Step 3 :
Equation at the end of step 3 :
((2x2 - x) - 6) (x + 4)
——————————————— ÷ ———————
(x2 + 3x) 2x + 3
Step 4 :
2x2 - x - 6
Simplify ———————————
x2 + 3x
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
x2 + 3x = x • (x + 3)
Trying to factor by splitting the middle term
5.2 Factoring 2x2 - x - 6
The first term is, 2x2 its coefficient is 2 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is -6
Step-1 : Multiply the coefficient of the first term by the constant 2 • -6 = -12
Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .
| -12 | + | 1 | = | -11 | ||
| -6 | + | 2 | = | -4 | ||
| -4 | + | 3 | = | -1 | That's it |
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3
2x2 - 4x + 3x - 6
Step-4 : Add up the first 2 terms, pulling out like factors :
2x • (x-2)
Add up the last 2 terms, pulling out common factors :
3 • (x-2)
Step-5 : Add up the four terms of step 4 :
(2x+3) • (x-2)
Which is the desired factorization
Equation at the end of step 5 :
(x - 2) • (2x + 3) (x + 4)
—————————————————— ÷ ———————
x • (x + 3) 2x + 3
Step 6 :
(x-2)•(2x+3) x+4
Divide ———————————— by ——————
x•(x+3) (2x+3)
6.1 Dividing fractions
To divide fractions, write the divison as multiplication by the reciprocal of the divisor :
(x - 2) • (2x + 3) x + 4 (x - 2) • (2x + 3) 2x + 3 —————————————————— ÷ ———————— = —————————————————— • ——————— x • (x + 3) (2x + 3) x • (x + 3) (x + 4)
Multiplying Exponential Expressions :
6.2 Multiply (2x + 3) by (2x + 3)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (2x+3) and the exponents are :
1 , as (2x+3) is the same number as (2x+3)1
and 1 , as (2x+3) is the same number as (2x+3)1
The product is therefore, (2x+3)(1+1) = (2x+3)2
Final result :
(x - 2) • (2x + 3)2
—————————————————————
x • (x + 3) • (x + 4)
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