x-a²-b²/c² + c²/x-a²-b²=2
Answers
Answer:0
Step-by-step explanation: x-a^2-b^2/c^2+c^2/x-a^2-b^2-(2)=0
Step by step solution :
Step 1 :
c2
Simplify ——
x
Equation at the end of step 1 :
(b2) c2
((x-(a2))-————)+——)-a2)-b2)-2 = 0
(c2) x
Step 2 :
b2
Simplify ——
c2
Equation at the end of step 2 :
b2 c2
(((((x-(a2))-——)+——)-a2)-b2)-2 = 0
c2 x
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using c2 as the denominator :
x - a2 (x - a2) • c2
x - a2 = —————— = —————————————
1 c2
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
Trying to factor as a Difference of Squares :
3.2 Factoring: x - a2
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 : x1 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares
Adding fractions that have a common denominator :
3.3 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:
(x-a2) • c2 - (b2) xc2 - a2c2 - b2
—————————————————— = ———————————————
c2 c2
Equation at the end of step 3 :
(xc2 - a2c2 - b2) c2
(((————————————————— + ——) - a2) - b2) - 2 = 0
c2 x
Step 4 :
Trying to factor a multi variable polynomial :
4.1 Factoring xc2 - a2c2 - b2
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Calculating the Least Common Multiple :
4.2 Find the Least Common Multiple
The left denominator is : c2
The right denominator is : x
Number of times each Algebraic
appears in the factorization of:
Algebraic
Factor Left
Denominator Right
Denominator L.C.M = Max
{Left,Right}
x 0 1 1
c 2 0 2
Least Common Multiple:
xc2
Calculating Multipliers :
4.3 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 = x
Right_M = L.C.M / R_Deno = c2
Making Equivalent Fractions :
4.4 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. (xc2-a2c2-b2) • x
————————————————— = ————
L.C.M xc2
R. Mult. • R. Num. c2 • c2
—————————————————— = ———————
L.C.M xc2
Adding fractions that have a common denominator :
4.5 Adding up the two equivalent fractions
(xc2-a2c2-b2) • x + c2 • c2 x2c2 - xa2c2 - xb2 + c4
= xc2 xc2
Equation at the end of step 4 :
(x2c2 - xa2c2 - xb2 + c4)
((————————————————————————— - a2) - b2) - 2 = 0
xc2
Step 5 :
Rewriting the whole as an Equivalent Fraction :
5.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using xc2 as the denominator :
a2 a2 • xc2
a2 = =
1 xc2
Checking for a perfect cube :
5.2 x2c2 - xa2c2 - xb2 + c4 is not a perfect cube
Adding fractions that have a common denominator :
5.3 Adding up the two equivalent fractions
(x2c2-xa2c2-xb2+c4) - (a2 • xc2) x2c2 - 2xa2c2 - xb2 + c4
———————————————————————————————— = ————————————————————————
xc2 xc2
Equation at the end of step 5 :
(x2c2 - 2xa2c2 - xb2 + c4)
(—————————————————————————— - b2) - 2 = 0
xc2
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using xc2 as the denominator :
b2 b2 • xc2
b2 = —— = ————————
1 xc2
Checking for a perfect cube :
6.2 x2c2 - 2xa2c2 - xb2 + c4 is not a perfect cube
Adding fractions that have a common denominator :
6.3 Adding up the two equivalent fractions
(x2c2-2xa2c2-xb2+c4) - (b2 • xc2) x2c2 - 2xa2c2 - xb2c2 - xb2 + c4
= xc2 xc2
Group 1: -xb2c2 + x2c2
Group 2: -2xa2c2 - 2xc2
Group 3: -xb2 + c4
Equation:
x2c2 - 2xa2c2 - xb2c2 - xb2 - 2xc2 + c4
= 0
xc2
When a fraction equals zero :
When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Here's how:
x2c2-2xa2c2-xb2c2-xb2-2xc2+c4
————————————————————————————— • xc2 = 0 • xc2
xc2
Now, on the left hand side, the xc2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
x2c2-2xa2c2-xb2c2-xb2-2xc2+c4 = 0
Solving a Single Variable Equation :
8.2 Solve x2c2-2xa2c2-xb2c2-xb2-2xc2+c4 = 0
Step-by-step explanation:
Taking LCM and cross multiplication brings it to the form (a+b+c+d)^2
