Solve...
(x+12) / (x+4) = (x) / (x+8)
cross multiply to clear the fractions and you have
(x+12)(x+8) = x(x+4)
x^2+20x+96 = x^2+4x
16x = -96
x = -6
I always appreciate showing how it is done.
To solve the given equation (x+12)/(x+4) = x/(x+8), we need to eliminate the denominators. Here's how you can do that:
Step 1: To eliminate the denominators, multiply both sides of the equation by the least common multiple (LCM) of (x+4) and (x+8). Since (x+4) and (x+8) have no common factors, their LCM is simply their product: (x+4)(x+8).
(x+12)/(x+4) * (x+4)(x+8) = x/(x+8) * (x+4)(x+8)
Simplifying both sides:
(x+12)(x+8) = x(x+4)
Step 2: Distribute and expand both sides of the equation.
(x^2 + 8x + 12x + 96) = x^2 + 4x
Simplifying further:
(x^2 + 20x + 96) = x^2 + 4x
Step 3: To solve for x, move all the terms to one side of the equation by subtracting x^2 and 4x from both sides.
x^2 + 20x + 96 - x^2 - 4x = 0
Simplifying:
16x + 96 = 0
Step 4: Subtract 96 from both sides of the equation.
16x = -96
Step 5: Divide both sides by 16 to solve for x.
x = -96/16
Simplifying:
x = -6
So the solution to the equation is x = -6.