solve it(p+p^1/3*q^2/3+p^2/3*q^1/3)/(p-q) * (p^1/3-q^1/3)/p^1/3
Answers
Answer:
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Answer:
Reformatting the input :
Changes made to your input should not affect the solution:
(1): Dot was discarded near ").(".
STEP
1
:
q
Simplify —
3
Equation at the end of step
1
:
((p•(q2))1) (((p2)•q)1) q
———————————)+———————————) ÷ (p-q)•(1-— ÷ p ÷ 3)
3 3 3
STEP
2
:
q
Divide — by p
3
Equation at the end of step
2
:
((p•(q2))1) (((p2)•q)1) q
———————————)+———————————) ÷ (p-q)•(1-—— ÷ 3)
3 3 3p
STEP
3
:
q
Divide —— by 3
3p
Equation at the end of step
3
:
((p•(q2))1) (((p2)•q)1) q
———————————)+———————————) ÷ (p-q)•(1-——)
3 3 9p
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 9p as the denominator :
1 1 • 9p
1 = — = ——————
1 9p
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 :
4.2 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:
9p - (q) 9p - q
———————— = ——————
9p 9p
Equation at the end of step
4
:
((p•(q2))1) (((p2)•q)1) (9p-q)
———————————)+———————————) ÷ (p-q)•——————
3 3 9p
STEP
5
:
p2q
Simplify ———
3
Equation at the end of step
5
:
((p•(q2))1) p2q (9p-q)
———————————)+———) ÷ (p-q)•——————
3 3 9p
STEP
6
:
pq2
Simplify ———
3
Equation at the end of step
6
:
pq2 p2q (9p - q)
———) + ———) ÷ (p - q) • ————————
3 3 9p
STEP
7
:
Rewriting the whole as an Equivalent Fraction :
7.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3 as the denominator :
p p • 3
p = — = —————
1 3
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
p • 3 + pq2 pq2 + 3p
——————————— = ————————
3 3
Equation at the end of step
7
:
(pq2 + 3p) p2q (9p - q)
—————————— + ———) ÷ (p - q) • ————————
3 3 9p
STEP
8
:
STEP
9
:
Pulling out like terms :
9.1 Pull out like factors :
pq2 + 3p = p • (q2 + 3)
Polynomial Roots Calculator :
9.2 Find roots (zeroes) of : F(q) = q2 + 3
Polynomial Roots Calculator is a set of methods aimed at finding values of q for which F(q)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers q 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 3.
The factor(s) are:
of the Leading Coefficient : 1
of the Trailing Constant : 1 ,3
Let us test ....
P Q P/Q F(P/Q) Divisor
-1 1 -1.00 4.00
-3 1 -3.00 12.00
1 1 1.00 4.00
3 1 3.00 12.00
Polynomial Roots Calculator found no rational roots
Adding fractions which have a common denominator :
9.3 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:
p • (q2+3) + p2q p2q + pq2 + 3p
———————————————— = ——————————————
3 3
Equation at the end of step
9
:
(p2q + pq2 + 3p) (9p - q)
———————————————— ÷ (p - q) • ————————
3 9p
STEP
10
:
p2q+pq2+3p
Divide —————————— by p-q
3
STEP
11
:
Pulling out like terms :
11.1 Pull out like factors :
p2q + pq2 + 3p = p • (pq + q2 + 3)
Trying to factor a multi variable polynomial :
11.2 Factoring pq + q2 + 3
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Equation at the end of step
11
:
p • (pq + q2 + 3) (9p - q)
————————————————— • ————————
3 • (p - q) 9p
STEP
12
:
Canceling Out :
12.1 Canceling out p as it appears on both sides of the fraction line