Problem 51

Question

For the following problems, solve the rational equations. $$ \frac{16}{y^{2}}=1 $$

Step-by-Step Solution

Verified
Answer
Question: Solve the rational equation: $\frac{16}{y^{2}}=1$. Answer: The possible values of y are y = 4 and y = -4.
1Step 1: Multiply both sides of the equation by y^2
To get rid of the fraction, we will multiply both sides of the equation by y^2. This will give us a new equation without a fraction: $$ y^2(\frac{16}{y^{2}})=y^2(1) $$
2Step 2: Simplify the equation
Now, let's simplify the equation by canceling out the terms on each side of the equation: $$ 16 = y^2 $$
3Step 3: Solve for y
To find the value of y, we need to find the square root of both sides of the equation: $$ y= \pm \sqrt{16} $$ The possible values of y are: $$ y= \pm 4 $$ So, the solution for the rational equation is y = 4 and y = -4.