(x+1/x)2-(x-1/x)2 anybody solve this with explain
Answers
Answer:
4-----x
Step-by-step explanation:
STEP
1
:
1
Simplify —
x
Equation at the end of step
1
:
1 1
((x+—)•2)-((x-—)•2)
x x
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x as the denominator :
x x • x
x = — = —————
1 x
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:
x • x - (1) x2 - 1
——————————— = ——————
x x
Equation at the end of step
2
:
1 (x2 - 1)
((x + —) • 2) - (———————— • 2)
x x
STEP
3
:
Trying to factor as a Difference of Squares:
3.1 Factoring: x2-1
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 : 1 is the square of 1
Check : x2 is the square of x1
Factorization is : (x + 1) • (x - 1)
Equation at the end of step
3
:
1 2•(x+1)•(x-1)
((x+—)•2)-—————————————
x x
STEP
4
:
1
Simplify —
x
Equation at the end of step
4
:
1 2•(x+1)•(x-1)
((x+—)•2)-—————————————
x x
STEP
5
:
Rewriting the whole as an Equivalent Fraction :
5.1 Adding a fraction to a whole
Rewrite the whole as a fraction using x as the denominator :
x x • x
x = — = —————
1 x
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
x • x + 1 x2 + 1
————————— = ——————
x x
Equation at the end of step
5
:
(x2 + 1) 2 • (x + 1) • (x - 1)
(———————— • 2) - —————————————————————
x x
STEP
6
:
Polynomial Roots Calculator :
6.1 Find roots (zeroes) of : F(x) = x2+1
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 1 and the Trailing Constant is 1.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 2.00
1 1 1.00 2.00
Polynomial Roots Calculator found no rational roots
Equation at the end of step
6
:
2 • (x2 + 1) 2 • (x + 1) • (x - 1)
———————————— - —————————————————————
x x
STEP
7
:
Adding fractions which have a common denominator :
7.1 Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
2 • (x2+1) - (2 • (x+1) • (x-1)) 4
———————————————————————————————— = —
x x
Final result :
4
—
x
another answer in photo
Answer:
2x +2/2-(2x-2/2)
=2x+2/2-2x+2/2
=2x+2-2x+2/2
=2+2/2=4/2=2
So 2 is answer