Question

Help!what is the least common denominator of 4/x^2y+5/y^2?

Answer 1

i can give you a problem that is the same but not the same numbers @Brookebrookiee

Answer 2

Okay, thank you, that works.

Answer 3

is x2 - x - 2 & x2 - 3x + 2 ok

Answer 4

Yes

Answer 5

6x+5y/x2+4xy+4y2/x+2y/5
Final result :

20x3y + 30x3 + 2x2y + 20xy2 + 25y
—————————————————————————————————
5x2

Step by step solution :
Step 1 :

Raise y to the 2nd power

Exponentiaion :

Equation at the end of step 1 :

y y2 2y
(((6x+(5•————))+4xy)+(4•——))+——
(x2) x 5

Step 2 :

Raise x to the 2nd power

Exponentiaion :

Equation at the end of step 2 :

y 4y2 2y
(((6x+(5•——))+4xy)+———)+——
x2 x 5

Step 3 :

5y
Simplify 6x + ——
x2

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 :

6x 6x • x2
6x = —— = ———————
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:

6x • x2 + 5y 6x3 + 5y
———————————— = ————————
x2 x2

Equation at the end of step 3 :

(6x3 + 5y) 4y2 2y
((—————————— + 4xy) + ———) + ——
x2 x 5

Step 4 :

6x3+5y
Simplify —————— + 4xy
x2

Rewriting the whole as an Equivalent Fraction :

4.1 Adding a whole to a fraction

Rewrite the whole as a fraction using x2 as the denominator :

4xy 4xy • x2
4xy = ——— = ————————
1 x2

Trying to factor as a Sum of Cubes :

4.2 Factoring: 6x3 + 5y

Theory : A sum 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 : 6 is not a cube !!

Ruling : Binomial can not be factored as the difference of two perfect cubes

Adding fractions that have a common denominator :

4.3 Adding up the two equivalent fractions

(6x3+5y) + 4xy • x2 4x3y + 6x3 + 5y
——————————————————— = ———————————————
x2 x2

Equation at the end of step 4 :

(4x3y + 6x3 + 5y) 4y2 2y
(————————————————— + ———) + ——
x2 x 5

Step 5 :

4x3y+6x3+5y 4y2
Simplify ——————————— + ———
x2 x

Trying to factor a multi variable polynomial :

5.1 Factoring 4x3y + 6x3 + 5y

Try to factor this multi-variable trinomial using trial and error

Factorization fails
Calculating the Least Common Multiple :

5.2 Find the Least Common Multiple

The left denominator is : x2

The right denominator is : x
Number of times each Algebraic Factor
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 2 1 2


Least Common Multiple:
x2
Calculating Multipliers :

5.3 Calculate multipliers for the two fractions


Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 1

Right_M = L.C.M / R_Deno = x

Making Equivalent Fractions :

5.4 Rewrite the two fractions into equivalent fractions

Two fractions are called equivalent if they have the same numeric value.

For example : 1/2 and 2/4 are equivalent, y/(y+1)2 and (y2+y)/(y+1)3 are equivalent as well.

To calculate equivalent fraction , multiply the Numerator of each fraction, by its respective Multiplier.

L. Mult. • L. Num. (4x3y+6x3+5y)
—————————————————— = —————————————
L.C.M x2

R. Mult. • R. Num. 4y2 • x
—————————————————— = ———————
L.C.M x2

Adding fractions that have a common denominator :

5.5 Adding up the two equivalent fractions

(4x3y+6x3+5y) + 4y2 • x 4x3y + 6x3 + 4xy2 + 5y
——————————————————————— = ——————————————————————
x2 x2

Equation at the end of step 5 :

(4x3y + 6x3 + 4xy2 + 5y) 2y
———————————————————————— + ——
x2 5

Step 6 :

4x3y+6x3+4xy2+5y 2y
Simplify ———————————————— + ——
x2 5

Checking for a perfect cube :

6.1 4x3y+6x3+4xy2+5y is not a perfect cube
Trying to factor a multi variable polynomial :

No factorization found
Calculating the Least Common Multiple :

6.2 Find the Least Common Multiple

The left denominator is : x2

The right denominator is : 5
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
5 0 1 1
Product of all
Prime Factors 1 5 5

Number of times each Algebraic Factor
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 2 0 2


Least Common Multiple:
5x2
Calculating Multipliers :

6.3 Calculate multipliers for the two fractions


Denote the Least Common Multiple by L.C.M
Denote the Left Multiplier by Left_M
Denote the Right Multiplier by Right_M
Denote the Left Deniminator by L_Deno
Denote the Right Multiplier by R_Deno

Left_M = L.C.M / L_Deno = 5

Right_M = L.C.M / R_Deno = x2

Making Equivalent Fractions :

6.4 Rewrite the two fractions into equivalent fractions

L. Mult. • L. Num. (4x3y+6x3+4xy2+5y) • 5
—————————————————— = ——————————————————————
L.C.M 5x2

R. Mult. • R. Num. 2y • x2
—————————————————— = ———————
L.C.M 5x2

Adding fractions that have a common denominator :

6.5 Adding up the two equivalent fractions

(4x3y+6x3+4xy2+5y) • 5 + 2y • x2 20x3y + 30x3 + 2x2y + 20xy2 + 25y
———————————————————————————————— = —————————————————————————————————
5x2 5x2

Final result :

20x3y + 30x3 + 2x2y + 20xy2 + 25y
—————————————————————————————————
5x2

Answer 6

well nevermind haha @Brookebrookiee

Answer 7

I still don't understand how I solve it?

Answer 8

@Jinx.exe will my answer be x+5?

Answer 9

look at the final result

Answer 10

It says 5x2?

Answer 11

it does