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Other Ways to Solve
Adding, subtracting and finding the least common multipleStep by Step Solution
Reformatting the input :
Changes made to your input should not affect the solution:
(1): "s1" was replaced by "s^1".
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
1/f-(1/s^1/s)=0
Step 1 :
1
Simplify —
s
Equation at the end of step 1 :
1 1
— - — ÷ s = 0
f s
Step 2 :
1
Divide — by s
s
Multiplying exponential expressions :
2.1 s1 multiplied by s1 = s(1 + 1) = s2
Equation at the end of step 2 :
1 1
— - —— = 0
f s2
Step 3 :
1
Simplify —
f
Equation at the end of step 3 :
1 1
— - —— = 0
f s2
Step 4 :
Calculating the Least Common Multiple :
4.1 Find the Least Common Multiple
The left denominator is : f
The right denominator is : s2
Algebraic Factor | Left Denominator | Right Denominator | L.C.M = Max {Left,Right} |
---|---|---|---|
f | 1 | 0 | 1 |
s | 0 | 2 | 2 |
Least Common Multiple:
fs2
Calculating Multipliers :
4.2 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 = s2
Right_M = L.C.M / R_Deno = f
Making Equivalent Fractions :
4.3 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. s2 —————————————————— = ——— L.C.M fs2 R. Mult. • R. Num. f —————————————————— = ——— L.C.M fs2
Adding fractions that have a common denominator :
4.4 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:
s2 - (f) s2 - f
———————— = ——————
fs2 fs2
Trying to factor as a Difference of Squares :
4.5 Factoring: s2 - f
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 : s2 is the square of s1
Check : f1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Equation at the end of step 4 :
s2 - f
—————— = 0
fs2
Step 5 :
When a fraction equals zero :
5.1 When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
s2-f
———— • fs2 = 0 • fs2
fs2
Now, on the left hand side, the fs2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
s2-f = 0
Solving a Single Variable Equation :
5.2 Solve -f+s2 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
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