The least common denominator (LCD) is the smallest number or expression that will be a common to given set of fractions :
For example :
1/a and 1/b
The LCD will be ab Since ab can be divided by a or b
From the given problem :
The denominators are x, x + 10 and 3
The LCD will be the product of these 3 denominators :
LCD = 3x(x + 10)
Now, Multiply this LCD to both sides of the equation :
Simplifying the equation :
3(x+10) + 2(3x) = x(x+10)
3x + 30 + 6x = x^2 + 10x
x^2 + x - 30 = 0
Factoring Completely :
Think of a number that has a product of -30 and a sum of +1
In this case, it is +6 and -5
(x + 6)(x - 5)=0
x + 6 = 0 => x = -6
x - 5 =0 => x = 5
So there are 2 valid solutions..
But you need to check it if there is an expression that will be undefined if you substitute the value of x:
By inspection, no fractions that will give you an undefined value..
But IF there is a value of x that gives you an undefined value. disregard that value of x.
For example.
IF you got x = -6 and x = -10
-6 will not give you an undefined value, but -10 will do.
since you have 2/(x + 10).. 2/(-10 + 10) = undefined.
So you only have 1 valid solution for this scenario.
