54[(3a+8)(9a-7)+2(2a+1/3a)(4a+1)-2a/3(1/a^2+165/2)]=31[(5+3a)(a-1/a)+(5/a+2)(1-4a) +3a] Find a?
Answers
Answer:
STEP
1
:
165
Simplify ———
2
Equation at the end of step
1
:
1 1 a 1 165
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-((2•—)•(—+———)))
3 a 3 a 2
STEP
2
:
1
Simplify —
a
Equation at the end of step
2
:
1 1 a 1 165
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-((2•—)•(—+———)))
3 a 3 a 2
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : a
The right denominator is : 2
Number of times each prime factor
appears in the factorization of:
Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
2 0 1 1
Product of all
Prime Factors 1 2 2
Number of times each Algebraic Factor
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
a 1 0 1
Least Common Multiple:
2a
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 = 2
Right_M = L.C.M / R_Deno = a
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. 2
—————————————————— = ——
L.C.M 2a
R. Mult. • R. Num. 165 • a
—————————————————— = ———————
L.C.M 2a
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:
2 + 165 • a 165a + 2
——————————— = ————————
2a 2a
Equation at the end of step
3
:
1 1 a (165a+2)
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-((2•—)•————————))
3 a 3 2a
STEP
4
:
a
Simplify —
3
Equation at the end of step
4
:
1 1 a (165a+2)
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-((2•—)•————————))
3 a 3 2a
STEP
5
:
Equation at the end of step
5
:
1 1 (165a+2)
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-————————)
3 a 3
STEP
6
:
1
Simplify —
a
Equation at the end of step
6
:
1 1 (165a+2)
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-————————)
3 a 3
STEP
7
:
1
Simplify —
3
Equation at the end of step
7
:
1 1 (165a+2)
54•((((3a+8)•(9a-7))+((2•(2a+(—•—)))•(4a+1)))-————————)
3 a 3
STEP
8
:
Rewriting the whole as an Equivalent Fraction :
8.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 3a as the denominator :
2a 2a • 3a
2a = —— = ———————
1 3a
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
Answer:
a=1
Step-by-step explanation:
We can substitute 'a' as 1