You can put this solution on YOUR website!
I think most would agree that an equation without fractions is easier than an equation with fractions. So we are going to start by eliminating the fractions.
Fractions can be eliminated from an equation by
Finding the Lowest Common Denominator (LCD) of all the fractions on both sides of the equation.
Multiply both sides of the equation by the LCD.
Since your two denominators, x+6 and x+4, have no common factors, the LCD will simply be their product. So we multiply both sides by the product of the two denominators:
The denominators cancel:
leaving
The fractions are now gone. To solve this equation we start by simplifying each side (using FOIL):
which simplifies to:
At first this may seem to be a quadratic equation because of the squared terms. But if we subtract from each side we get:
9x + 20 = 4x + (-12)
and the squared terms are gone. So it is not a quadratic equation. We start the solution by subtracting 4x from each side:
5x + 20 = (-12)
Subtracting 20 from each side we get:
5x = -32
Dividing by 5 we get:
x =
The only thing left to do is to check your answer. Whenever you multiply both sides by an equation by an expression that could be zero, like we did when we multiplied by the LCD, you must check your answers. The main thing to check is that your answers do not make a denominator zero. I think we can easily see that if x = -32/5 that both denominators, x+5 and x+4, will not be zero. So our answer looks good. (If a denominator had been zero when x = -32/5, then we would have to reject the solution.) The full check will tell us if we made a mistake. You are welcome to finish the check if you like.
P.S. Please put multiply term numerators and denominators in parentheses:
(x+5)/(x+6)=(x-2)/(x+4)
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