Question

solve the rational equation: $\frac{1}{4}=\frac{5x + 20}{4x + 12}-\frac{1}{4x + 12}$
$x=-4$
$x=-1$
$x = 1$
$x = 4$

Explanation:

Step1: Combine right - hand side fractions

Since the denominators of the two fractions on the right - hand side are the same ($4x + 12$), we have $\frac{5x + 20}{4x+12}-\frac{1}{4x + 12}=\frac{5x+20 - 1}{4x + 12}=\frac{5x+19}{4x + 12}$. So the equation becomes $\frac{1}{4}=\frac{5x + 19}{4x+12}$.

Step2: Cross - multiply

Cross - multiplying gives us $4(5x + 19)=1\times(4x + 12)$.
Expanding both sides: $20x+76 = 4x+12$.

Step3: Isolate the variable terms

Subtract $4x$ from both sides: $20x-4x+76=4x - 4x+12$, which simplifies to $16x+76 = 12$.
Then subtract 76 from both sides: $16x+76-76=12 - 76$, so $16x=-64$.

Step4: Solve for x

Divide both sides by 16: $x=\frac{-64}{16}=-4$. But we need to check for extraneous solutions.
When $x = - 4$, the denominator $4x+12=4\times(-4)+12=-16 + 12=-4
eq0$.

Answer:

$x=-4$