multiply (x + 1/x) (x+1/x)
Answers
Answer:
x^2 + 1/x^2 +2 is the answer
Answer:
STEP
1
:
1
Simplify —
x
Equation at the end of step
1
:
1 1
(x + —) • (x + —)
x x
STEP
2
:
Rewriting the whole as an Equivalent Fraction
2.1 Adding a fraction to 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 + —) • ————————
x x
STEP
3
:
1
Simplify —
x
Equation at the end of step
3
:
1 (x2 + 1)
(x + —) • ————————
x x
STEP
4
:
Rewriting the whole as an Equivalent Fraction :
4.1 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 :
4.2 Adding up the two equivalent fractions
x • x + 1 x2 + 1
————————— = ——————
x x
Equation at the end of step
4
:
(x2 + 1) (x2 + 1)
———————— • ————————
x x
STEP
5
:
Polynomial Roots Calculator :
5.1 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
Polynomial Roots Calculator :
5.2 Find roots (zeroes) of : F(x) = x2+1
See theory in step 5.1
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
Multiplying exponential expressions :
5.3 x1 multiplied by x1 = x(1 + 1) = x2
Multiplying Exponential Expressions:
5.4 Multiply (x2+1) by (x2+1)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x2+1) and the exponents are :
1 , as (x2+1) is the same number as (x2+1)1
and 1 , as (x2+1) is the same number as (x2+1)1
The product is therefore, (x2+1)(1+1) = (x2+1)2
Final result :
(x2 + 1)2
—————————
x2