Answer:
3 • (4y + 15)
-----------------
40
Explanation:
Long explanation get ready
STEP
1
:
7
Simplify —
8
Equation at the end of step
1
:
1 9 3 7
((—+(——•y))-(—•y))+—
4 10 5 8
STEP
2
:
3
Simplify —
5
Equation at the end of step
2
:
1 9 3 7
((—+(——•y))-(—•y))+—
4 10 5 8
STEP
3
:
9
Simplify ——
10
Equation at the end of step
3
:
1 9 3y 7
((— + (—— • y)) - ——) + —
4 10 5 8
STEP
4
:
1
Simplify —
4
Equation at the end of step
4
:
1 9y 3y 7
((— + ——) - ——) + —
4 10 5 8
STEP
5
:
Calculating the Least Common Multiple :
5.1 Find the Least Common Multiple
The left denominator is : 4
The right denominator is : 10
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 1 2
5 0 1 1
Product of all
Prime Factors 4 10 20
Least Common Multiple:
20
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 = 5
Right_M = L.C.M / R_Deno = 2
Making Equivalent Fractions :
5.3 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. 5
—————————————————— = ——
L.C.M 20
R. Mult. • R. Num. 9y • 2
—————————————————— = ——————
L.C.M 20
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 denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5 + 9y • 2 18y + 5
—————————— = ———————
20 20
Equation at the end of step
5
:
(18y + 5) 3y 7
(————————— - ——) + —
20 5 8
STEP
6
:
Calculating the Least Common Multiple :
6.1 Find the Least Common Multiple
The left denominator is : 20
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}
2 2 0 2
5 1 1 1
Product of all
Prime Factors 20 5 20
Least Common Multiple:
20
Calculating Multipliers :
6.2 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 = 4
Making Equivalent Fractions :
6.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (18y+5)
—————————————————— = ———————
L.C.M 20
R. Mult. • R. Num. 3y • 4
—————————————————— = ——————
L.C.M 20
Adding fractions that have a common denominator :
6.4 Adding up the two equivalent fractions
(18y+5) - (3y • 4) 6y + 5
—————————————————— = ——————
20 20
Equation at the end of step
6
:
(6y + 5) 7
———————— + —
20 8
STEP
7
:
Calculating the Least Common Multiple :
7.1 Find the Least Common Multiple
The left denominator is : 20
The right denominator is : 8
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 2 3 3
5 1 0 1
Product of all
Prime Factors 20 8 40
Least Common Multiple:
40
Calculating Multipliers :
7.2 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 = 2
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
7.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (6y+5) • 2
—————————————————— = ——————————
L.C.M 40
R. Mult. • R. Num. 7 • 5
—————————————————— = —————
L.C.M 40
Adding fractions that have a common denominator :
7.4 Adding up the two equivalent fractions
(6y+5) • 2 + 7 • 5 12y + 45
—————————————————— = ————————
40 40
STEP
8
:
Pulling out like terms :
8.1 Pull out like factors :
12y + 45 = 3 • (4y + 15)