Question
Solve the following rational equation for X: x^2 over x+5= 25 over x+5
Answers
GPT-4o mini
To solve the rational equation
\[
\frac{x^2}{x+5} = \frac{25}{x+5},
\]
we can first eliminate the denominator (assuming \(x + 5 \neq 0\)) by multiplying both sides by \(x + 5\):
\[
x^2 = 25.
\]
Next, we solve the equation \(x^2 = 25\) by taking the square root of both sides:
\[
x = \pm 5.
\]
Now we have two potential solutions: \(x = 5\) and \(x = -5\).
However, we need to check if any of these solutions would make the original denominator zero, which would be problematic. The denominator \(x + 5 = 0\) when \(x = -5\). Thus, \(x = -5\) is not a valid solution.
The only valid solution is
\[
x = 5.
\]
Therefore, the solution to the equation is
\[
\boxed{5}.
\]
\[
\frac{x^2}{x+5} = \frac{25}{x+5},
\]
we can first eliminate the denominator (assuming \(x + 5 \neq 0\)) by multiplying both sides by \(x + 5\):
\[
x^2 = 25.
\]
Next, we solve the equation \(x^2 = 25\) by taking the square root of both sides:
\[
x = \pm 5.
\]
Now we have two potential solutions: \(x = 5\) and \(x = -5\).
However, we need to check if any of these solutions would make the original denominator zero, which would be problematic. The denominator \(x + 5 = 0\) when \(x = -5\). Thus, \(x = -5\) is not a valid solution.
The only valid solution is
\[
x = 5.
\]
Therefore, the solution to the equation is
\[
\boxed{5}.
\]
sayletyler
Few things, I need it simplified down to like 4 sentnces also can you say fractions like I did in my original question like x^2 Over the over is what im concerned about also {} these things and also any double parentesis I dont want them to know an Ai answered this
GPT-4o mini
To solve the rational equation \(\frac{x^2}{x+5} = \frac{25}{x+5}\), we first multiply both sides by \(x+5\) (assuming \(x \neq -5\)), resulting in \(x^2 = 25\). We then solve for \(x\), giving \(x = 5\) and \(x = -5\). However, \(x = -5\) makes the denominator zero, so it’s not a valid solution. Thus, the solution to the equation is \(\{5\}\).
sayletyler
Oh and no backwards slashes and I think i still see some of these {}
GPT-4o mini
To solve the rational equation x^2 over x + 5 = 25 over x + 5, we first multiply both sides by x + 5 (assuming x is not equal to -5), resulting in x^2 = 25. We then solve for x, giving us x = 5 and x = -5. However, x = -5 makes the denominator zero, so it’s not a valid solution. Therefore, the solution to the equation is 5.
sayletyler
That works thank you
GPT-4o mini
You're welcome! If you have any more questions or need further assistance, feel free to ask. Good luck!