Add (2m^2n + 5mn^2 - 7mn) ; (2m^2n - mn^2 + mn

Step-by-step explanation:

(3m+2n)/(m-n2)+(5m+n)/(n-m2)-(2m-3n)/(m2-n)

Final result :

-3m3 - 2m2n + 7m2 - 7mn2 + mn + 2n3 + 2n2

—————————————————————————————————————————

(m - n2) • (n - m2)

Step by step solution :

Step 1 :

2m - 3n

Simplify ———————

m2 - n

Trying to factor as a Difference of Squares :

1.1 Factoring: m2 - n

Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)

Proof : (A+B) • (A-B) =

A2 - AB + BA - B2 =

A2 - AB + AB - B2 =

A2 - B2

Note : AB = BA is the commutative property of multiplication.

Note : - AB + AB equals zero and is therefore eliminated from the expression.

Check : m2 is the square of m1

Check : n1 is not a square !!

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

Equation at the end of step 1 :

(3m+2n) (5m+n) (2m-3n)

(————————+————————)-———————

(m-(n2)) (n-(m2)) m2-n

Step 2 :

5m + n

Simplify ——————

n - m2

Trying to factor as a Difference of Squares :

2.1 Factoring: n - m2

Check : n1 is not a square !!

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

Equation at the end of step 2 :

(3m+2n) (5m+n) (2m-3n)

(————————+——————)-———————

(m-(n2)) n-m2 m2-n

Step 3 :

3m + 2n

Simplify ———————

m - n2

Trying to factor as a Difference of Squares :

3.1 Factoring: m - n2

Check : m1 is not a square !!

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

Equation at the end of step 3 :

(3m + 2n) (5m + n) (2m - 3n)

(————————— + ————————) - —————————

m - n2 n - m2 m2 - n

Step 4 :

Calculating the Least Common Multiple :

4.1 Find the Least Common Multiple

The left denominator is : m-n2

The right denominator is : n-m2

Number of times each Algebraic Factor

appears in the factorization of:

Algebraic

Factor Left

Denominator Right

Denominator L.C.M = Max

{Left,Right}

m-n2 1 0 1

n-m2 0 1 1

Least Common Multiple:

(m-n2) • (n-m2)

Calculating Multipliers :

4.2 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 = n-m2

Right_M = L.C.M / R_Deno = m-n2

what is the question? i am guessing you are looking for the area.

to find an area, you have to do length x width.

in this case, it would be 12 ft x 4 ft = 48 sq. ft

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!