solve 1/x + 1/(x-6) = 1/4
Answers
Answer:
Step by step solution :
STEP1:
1 Simplify — 4
Equation at the end of step1:
1 1 1 (— + —) - — = 0 x 6 4
STEP2:
1 Simplify — 6
Equation at the end of step2:
1 1 1 (— + —) - — = 0 x 6 4
STEP3:
1 Simplify — x
Equation at the end of step3:
1 1 1 (— + —) - — = 0 x 6 4
STEP4:Calculating the Least Common Multiple
4.1 Find the Least Common Multiple
The left denominator is : x
The right denominator is : 6
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 20113011 Product of all
Prime Factors 166
Number of times each Algebraic Factor
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} x 101
Least Common Multiple:
6x
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 = 6
Right_M = L.C.M / R_Deno = x
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. 6 —————————————————— = —— L.C.M 6x R. Mult. • R. Num. x —————————————————— = —— L.C.M 6x
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:
6 + x x + 6 ————— = ————— 6x 6x
Equation at the end of step4:
(x + 6) 1 ——————— - — = 0 6x 4
STEP5:Calculating the Least Common Multiple
5.1 Find the Least Common Multiple
The left denominator is : 6x
The right denominator is : 4
Number of times each prime factor
appears in the factorization of: Prime
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} 21223101 Product of all
Prime Factors 6412
Number of times each Algebraic Factor
appears in the factorization of: Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right} x 101
Least Common Multiple:
12x
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 = 2
Right_M = L.C.M / R_Deno = 3x
Making Equivalent Fractions :
5.3 Rewrite the two fractions into equivalent fractions
L. Mult. • L. Num. (x+6) • 2 —————————————————— = ————————— L.C.M 12x R. Mult. • R. Num. 3x —————————————————— = ——— L.C.M 12x
Adding fractions that have a common denominator :
5.4 Adding up the two equivalent fractions
(x+6) • 2 - (3x) 12 - x ———————————————— = —————— 12x 12x
Equation at the end of step5:
12 - x —————— = 0 12x
STEP6:When a fraction equals zero
6.1 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:
12-x ———— • 12x = 0 • 12x 12x
Now, on the left hand side, the 12x cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
12-x = 0
Solving a Single Variable Equation:
6.2 Solve : -x+12 = 0
Subtract 12 from both sides of the equation :
-x = -12
Multiply both sides of the equation by (-1) : x = 12