17x-53/x^2-2x-15 equals
Answers
Answer:
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Step-by-step explanation:
STEP1:
53 Simplify —— x2
Equation at the end of step1:
53 ((17x - ——) - 2x) - 15 x2
STEP2:Rewriting the whole as an Equivalent Fraction
2.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x2 as the denominator :
17x 17x • x2 17x = ——— = ———————— 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:
17x • x2 - (53) 17x3 - 53 ——————————————— = ————————— x2 x2
Equation at the end of step2:
(17x3 - 53) (——————————— - 2x) - 15 x2
STEP3:
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x2 as the denominator :
2x 2x • x2 2x = —— = ——————— 1 x2
Trying to factor as a Difference of Cubes:
3.2 Factoring: 17x3 - 53
Theory : A difference of two perfect cubes, a3 - b3 can be factored into
(a-b) • (a2 +ab +b2)
Proof : (a-b)•(a2+ab+b2) =
a3+a2b+ab2-ba2-b2a-b3 =
a3+(a2b-ba2)+(ab2-b2a)-b3 =
a3+0+0-b3 =
a3-b3
Check : 17 is not a cube !!
Ruling : Binomial can not be factored as the difference of two perfect cubes
Polynomial Roots Calculator :
3.3 Find roots (zeroes) of : F(x) = 17x3 - 53
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 17 and the Trailing Constant is -53.
The factor(s) are:
of the Leading Coefficient : 1,17
of the Trailing Constant : 1 ,53
Adding fractions that have a common denominator :
4.4 Adding up the two equivalent fractions
(15x3-53) - (15 • x2) 15x3 - 15x2 - 53 ————————————————————— = ———————————————— x2 x2
Polynomial Roots Calculator :
4.5 Find roots (zeroes) of : F(x) = 15x3 - 15x2 - 53
See theory in step 3.3
In this case, the Leading Coefficient is 15 and the Trailing Constant is -53.
The factor(s) are:
of the Leading Coefficient : 1,3 ,5 ,15
of the Trailing Constant : 1 ,53
Polynomial Roots Calculator found no rational roots