find y if 2y-3/4 -3y-5/2 =y+3/4
with explaination
Answers
Explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
3*y/5-2*y/3-(4)=0
Step by step solution :
STEP
1
:
y
Simplify —
3
Equation at the end of step
1
:
y y
((3 • —) - (2 • —)) - 4 = 0
5 3
STEP
2
:
y
Simplify —
5
Equation at the end of step
2
:
y 2y
((3 • —) - ——) - 4 = 0
5 3
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : 5
The right denominator is : 3
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
5 1 0 1
3 0 1 1
Product of all
Prime Factors 5 3 15
Least Common Multiple:
15
Calculating Multipliers :
3.2 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 = 3
Right_M = L.C.M / R_Deno = 5
Making Equivalent Fractions :
3.3 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. 3y • 3
—————————————————— = ——————
L.C.M 15
R. Mult. • R. Num. 2y • 5
—————————————————— = ——————
L.C.M 15
Adding fractions that have a common denominator :
3.4 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:
3y • 3 - (2y • 5) -y
————————————————— = ——
15 15
Equation at the end of step
3
:
-y
—— - 4 = 0
15
STEP
4
:
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 15 as the denominator :
4 4 • 15
4 = — = ——————
1 15
Answer:
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Explanation:
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