simplify:-
(a^2-1/b^2)^a ×(a-1/b)^b-a /(b^2-1/a^2)^b (b+1/b)a-b
Answers
Answer:
Step by Step Solution
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STEP
1
:
1
Simplify —
b
Equation at the end of step
1
:
)1 1
——-—)
(a b
STEP
2
:
1
Simplify —
a
Equation at the end of step
2
:
)1 1
—— - —)
(a b
STEP
3
:
Calculating the Least Common Multiple :
3.1 Find the Least Common Multiple
The left denominator is : a
The right denominator is : b
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
b 0 1 1
Least Common Multiple:
ab
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 = b
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. b
—————————————————— = ——
L.C.M ab
R. Mult. • R. Num. a
—————————————————— = ——
L.C.M ab
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:
b - (a) b - a
——————— = —————
ab ab
Equation at the end of step
3
:
(b - a)
———————
ab
STEP
4
:
b-a
Divide a2-b2 by ———
ab
Trying to factor as a Difference of Squares:
4.1 Factoring: a2 - b2
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 : a2 is the square of a1
Check : b2 is the square of b1
Factorization is : (a + b) • (a - b)
4.2 Rewrite (b-a) as (-1) • (a-b)
Canceling Out :
4.3 Cancel out (a-b) which now appears on both sides of the fraction line.