x²+1/2x2=3
- Х - 1/x=?
Answers
Answer:
1.1 Factoring x2 - x + 2
The first term is, x2 its coefficient is 1 .
The middle term is, -x its coefficient is -1 .
The last term, "the constant", is +2
Step-1 : Multiply the coefficient of the first term by the constant 1 • 2 = 2
Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is -1 .
-2 + -1 = -3
-1 + -2 = -3
1 + 2 = 3
2 + 1 = 3
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
1.2 Attempting Polynomial Long Division
Attempted Long division of
x2-x+2
By :
1-x
Was aborted due to the followinf reason :
Dividend and Divisor do not share same variable
Equation at the end of step
1
:
(((2•(x2))-3x)-1) (x2-x+2)
—————————————————-————————
(x-1) 1-x
STEP
2
:
Equation at the end of step
2
:
((2x2 - 3x) - 1) (x2 - x + 2)
———————————————— - ————————————
(x - 1) 1 - x
STEP
3
:
2x2 - 3x - 1
Simplify ————————————
x - 1
Trying to factor by splitting the middle term
3.1 Factoring 2x2 - 3x - 1
The first term is, 2x2 its coefficient is 2 .
The middle term is, -3x its coefficient is -3 .
The last term, "the constant", is -1
Step-1 : Multiply the coefficient of the first term by the constant 2 • -1 = -2
Step-2 : Find two factors of -2 whose sum equals the coefficient of the middle term, which is -3 .
-2 + 1 = -1
-1 + 2 = 1
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Polynomial Long Division :
3.2 Polynomial Long Division
Dividing : 2x2-3x-1
("Dividend")
By : x-1 ("Divisor")
dividend 2x2 - 3x - 1
- divisor * 2x1 2x2 - 2x
remainder - x - 1
- divisor * -x0 - x + 1
remainder - 2
Quotient : 2x-1
Remainder : -2
Equation at the end of step
3
:
(2x2 - 3x - 1) (x2 - x + 2)
—————————————— - ————————————
x - 1 1 - x
STEP
4
:
Making Equivalent Fractions :
4.1 Rewrite the two fractions into equivalent fractions
Two fractions are called equivalent if they have the same numeric value.
For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.
To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.
L. Mult. • L. Num. (2x2-3x-1)
—————————————————— = ——————————
L.C.M x-1
R. Mult. • R. Num. (x2-x+2) • -1
—————————————————— = —————————————
L.C.M x-1
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:
(2x2-3x-1) - ((x2-x+2) • -1) 3x2 - 4x + 1
———————————————————————————— = ————————————
x-1 x - 1
Trying to factor by splitting the middle term
4.3 Factoring 3x2 - 4x + 1
The first term is, 3x2 its coefficient is 3 .
The middle term is, -4x its coefficient is -4 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 3 • 1 = 3
Step-2 : Find two factors of 3 whose sum equals the coefficient of the middle term, which is -4 .
-3 + -1 = -4 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -3 and -1
3x2 - 3x - 1x - 1
Step-4 : Add up the first 2 terms, pulling out like factors :
3x • (x-1)
Add up the last 2 terms, pulling out common factors :
1 • (x-1)
Step-5 : Add up the four terms of step 4 :
(3x-1) • (x-1)
Which is the desired factorization
Canceling Out :
4.4 Cancel out (x-1) which appears on both sides of the fraction line.
Final result :
3x - 1
Step-by-step explanation:
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