solution of x+ 1 = 18 and × /2 + 1 = 9 is same
Answers
Step-by-step explanation:
18
Simplify ——
x2
Equation at the end of step
1
:
9 18
((— - 1) + 1) - (—— - 1) = 0
x x2
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x2 as the denominator :
1 1 • x2
1 = — = ——————
1 x2
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 :
2.2 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:
18 - (x2) 18 - x2
————————— = ———————
x2 x2
Equation at the end of step
2
:
9 (18 - x2)
((— - 1) + 1) - ————————— = 0
x x2
STEP
3
:
9
Simplify —
x
Equation at the end of step
3
:
9 (18 - x2)
((— - 1) + 1) - ————————— = 0
x x2
STEP
4
:
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x as the denominator :
1 1 • x
1 = — = —————
1 x
Adding fractions that have a common denominator :
4.2 Adding up the two equivalent fractions
9 - (x) 9 - x
——————— = —————
x x
Equation at the end of step
4
:
(9 - x) (18 - x2)
(——————— + 1) - ————————— = 0
x x2
STEP
5
:
Rewriting the whole as an Equivalent Fraction :
5.1 Adding a whole to a fraction
Rewrite the whole as a fraction using x as the denominator :
1 1 • x
1 = — = —————
1 x
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
(9-x) + x 9
————————— = —
x x
Equation at the end of step
5
:
9 (18 - x2)
— - ————————— = 0
x x2
STEP
6
:
Trying to factor as a Difference of Squares:
6.1 Factoring: 18-x2
Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
Proof : (A+B) • (A-B) =
A2 - AB + BA - B2 =
A2 - AB + AB - B2 =
A2 - B2
Note : AB = BA is the commutative property of multiplication.
Note : - AB + AB equals zero and is therefore eliminated from the expression.
Check : 18 is not a square !!
Ruling : Binomial can not be factored as the
difference of two perfect squares
Calculating the Least Common Multiple :
6.2 Find the Least Common Multiple
The left denominator is : x
The right denominator is : x2
Answer:
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