Solve Addingsubtractingfindingleastcommonmultiple G/(g2-h2)

Reformatting the input :

Changes made to your input should not affect the solution: (1): "h2" was replaced by "h^2". 1 more similar replacement(s).

Step 1 :

h Simplify ————— g - h

Equation at the end of step 1 :

g h ———————————-((g•———)•2) ((g2)-(h2)) g-h

Step 2 :

Equation at the end of step 2 :

g gh ———————————-(———•2) ((g2)-(h2)) g-h

Step 3 :

Equation at the end of step 3 :

g 2gh ————————————— - ————— ((g2) - (h2)) g - h

Step 4 :

g Simplify ——————— g2 - h2

Trying to factor as a Difference of Squares :

4.1 Factoring: g2 - h2 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 - B2Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : g2 is the square of g1 Check : h2 is the square of h1 Factorization is : (g + h) • (g - h)

Equation at the end of step 4 :

g 2gh ————————————————— - ————— (g + h) • (g - h) g - h

Step 5 :

Calculating the Least Common Multiple :

5.1 Find the Least Common Multiple The left denominator is : (g+h) • (g-h) The right denominator is : g-h

Number of times each Algebraic Factor appears in the factorization of:

Algebraic Factor	Left Denominator	Right Denominator	L.C.M = Max {Left,Right}
g+h	1	0	1
g-h	1	1	1

Least Common Multiple: (g+h) • (g-h)

Calculating Multipliers :

5.2 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 = 1 Right_M = L.C.M / R_Deno = g+h

Making Equivalent Fractions :

5.3 Rewrite the two fractions into equivalent fractionsTwo 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. g —————————————————— = ————————————— L.C.M (g+h) • (g-h) R. Mult. • R. Num. 2gh • (g+h) —————————————————— = ————————————— L.C.M (g+h) • (g-h)

Adding fractions that have a common denominator :

5.4 Adding up the two equivalent fractions Add the two equivalent fractions which now have a common denominatorCombine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

g - (2gh • (g+h)) -2g2h - 2gh2 + g ————————————————— = ————————————————— (g+h) • (g-h) (g + h) • (g - h)

Step 6 :

Pulling out like terms :

6.1 Pull out like factors : -2g2h - 2gh2 + g = -g • (2gh + 2h2 - 1)

Trying to factor a multi variable polynomial :

6.2 Factoring 2gh + 2h2 - 1 Try to factor this multi-variable trinomial using trial and errorFactorization fails

Final result :

+g • (2gh + 2h2 + 1) ———————————————————— (g + h) • (g + h)