8
——
x2
Step-by-step explanation:
Equation at the end of step 1 :
8
y - (—— - 25) = 0
x2
Step 2 :
Rewriting the whole as an Equivalent Fraction :
2.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using x2 as the denominator :
25 25 • x2
25 = —— = ———————
1 x2
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
Adding fractions that have a common denominator :
2.2 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:
8 - (25 • x2) 8 - 25x2
————————————— = ————————
x2 x2
Equation at the end of step 2 :
(8 - 25x2)
y - —————————— = 0
x2
Step 3 :
Rewriting the whole as an Equivalent Fraction :
3.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using x2 as the denominator :
y y • x2
y = — = ——————
1 x2
Trying to factor as a Difference of Squares :
3.2 Factoring: 8 - 25x2
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 : 8 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
y • x2 - ((8-25x2)) yx2 + 25x2 - 8
——————————————————— = ——————————————
x2 x2
Trying to factor a multi variable polynomial :
3.4 Factoring yx2 + 25x2 - 8
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Equation at the end of step 3 :
yx2 + 25x2 - 8
—————————————— = 0
x2
Step 4 :
When a fraction equals zero :
4.1 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:
yx2+25x2-8
—————————— • x2 = 0 • x2
x2
Now, on the left hand side, the x2 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
yx2+25x2-8 = 0
Solving a Single Variable Equation :
4.2 Solve yx2+25x2-8 = 0
