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.
Other exercises in this chapter
Problem 51
For the following problems, perform the indicated operations. $$ \frac{15 y-4}{8 y+1}-\frac{2 y+1}{8 y+1} $$
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For the following problems, perform the divisions. $$ \frac{x^{3}+2 x+1}{x-3} $$
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For the following problems, replace \(N\) with the proper quantity. $$ \frac{x+2}{x-2}=\frac{N}{x^{2}-4} $$
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For the following problems, perform the multiplications and divisions. $$ (y-2) \div \frac{y-2}{y-1} $$
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