Factorise : x² + 1/x2-3x+3/x
Answers
Answer:
Given : x
2
+
x
2
1
−2−3x+
x
3
We can further write it as
x
2
+
x
2
1
−2−3x+
x
3
=(x−
x
1
)
2
−3(x−
x
1
)
By taking the common terms out
x
2
+
x
2
1
−2−3x+
x
3
=(x−
x
1
)(x−
x
1
−3)
Answer:
STEP
1
:
3
Simplify —
x
Equation at the end of step
1
:
1 3
(((x2)+————)-3x)+—
(x2) x
STEP
2
:
1
Simplify ——
x2
Equation at the end of step
2
:
1 3
(((x2) + ——) - 3x) + —
x2 x
STEP
3
:
Rewriting the whole as an Equivalent Fraction :
3.1 Adding a fraction to a whole
Rewrite the whole as a fraction using x2 as the denominator :
x2 x2 • x2
x2 = —— = ———————
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 :
3.2 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:
x2 • x2 + 1 x4 + 1
——————————— = ——————
x2 x2
Equation at the end of step
3
:
(x4 + 1) 3
(———————— - 3x) + —
x2 x
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x2 as the denominator :
3x 3x • x2
3x = —— = ———————
1 x2
Polynomial Roots Calculator :
4.2 Find roots (zeroes) of : F(x) = x4 + 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
Adding fractions that have a common denominator :
4.3 Adding up the two equivalent fractions
(x4+1) - (3x • x2) x4 - 3x3 + 1
—————————————————— = ————————————
x2 x2
Equation at the end of step
4
:
(x4 - 3x3 + 1) 3
—————————————— + —
x2 x
Step-by-step explanation:
please mark this answer as a brainliest.