Subtract the rational expressions to find the difference: x^2-2 over 4x-7 minus x+4 over 4x-7

Answer 1

To subtract the rational expressions \(\frac{x^2 - 2}{4x - 7}\) and \(\frac{x + 4}{4x - 7}\), we can combine them since they have the same denominator.

The expression is as follows:

\[ \frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7} \]

Since the denominators are the same, we can write:

\[ \frac{(x^2 - 2) - (x + 4)}{4x - 7} \]

Now, let's simplify the numerator:

1. Distribute the negative sign: \[ (x^2 - 2) - (x + 4) = x^2 - 2 - x - 4 \]

2. Combine like terms: \[ x^2 - x - 2 - 4 = x^2 - x - 6 \]

Now, we substitute back into our expression:

\[ \frac{x^2 - x - 6}{4x - 7} \]

Next, we can try to factor the numerator \(x^2 - x - 6\):

To factor \(x^2 - x - 6\), we need two numbers that multiply to \(-6\) and add up to \(-1\). Those numbers are \(-3\) and \(2\). So we can write:

\[ x^2 - x - 6 = (x - 3)(x + 2) \]

Substituting this back into the expression, we get:

\[ \frac{(x - 3)(x + 2)}{4x - 7} \]

Therefore, the final answer for the difference is:

\[ \frac{(x - 3)(x + 2)}{4x - 7} \]

Answer 2

Not an answer come on I made the question stupid simple

Answer 3

I'm sorry if my previous answer was more detailed than you expected. Let's simplify it step by step more straightforwardly.

You want to subtract the following rational expressions:

\[ \frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7} \]

Since both fractions have the same denominator, you can simply combine the numerators:

\[ \frac{(x^2 - 2) - (x + 4)}{4x - 7} \]

Now, simplify the numerator:

1. Distribute the negative sign: \[ x^2 - 2 - x - 4 = x^2 - x - 6 \]

So you now have:

\[ \frac{x^2 - x - 6}{4x - 7} \]

If you want to factor the numerator, \(x^2 - x - 6\), you can factor it as:

\[ (x - 3)(x + 2) \]

Thus, the expression simplifies to:

\[ \frac{(x - 3)(x + 2)}{4x - 7} \]

If you are looking for just the combined expression without factoring:

\[ \frac{x^2 - x - 6}{4x - 7} \]

Thanks for your patience, and let me know if you need any more help!

Answer 4

You combined 2 of my options together

Answer 5

I apologize for any confusion. Let's directly work on the expressions you provided without combining or simplifying anything excessively.

You have:

\[ \frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7} \]

Since both fractions have the same denominator \(4x - 7\), you can simply subtract the numerators. It can be rewritten as:

\[ \frac{(x^2 - 2) - (x + 4)}{4x - 7} \]

Next, simplify the numerator:

1. Expand the expression in the parentheses: \[ (x^2 - 2) - (x + 4) = x^2 - 2 - x - 4 \]

2. Combine like terms: \[ x^2 - x - 6 \]

Putting it all together, you have:

\[ \frac{x^2 - x - 6}{4x - 7} \]

If you prefer to leave it without factoring, this is the final expression.

If you need further assistance or clarification, please let me know!

Answer 6

No thats not it

Answer 7

I apologize for the confusion in my previous responses. Let's directly solve the subtraction you provided step by step:

You have:

\[ \frac{x^2 - 2}{4x - 7} - \frac{x + 4}{4x - 7} \]

Since both fractions have the same denominator, you can combine them directly:

\[ \frac{(x^2 - 2) - (x + 4)}{4x - 7} \]

Now, simplify the numerator properly. Let's break it down carefully:

1. Start with the numerator: \[ (x^2 - 2) - (x + 4) \]

2. Distributing the negative sign: \[ = x^2 - 2 - x - 4 \]

3. Combine like terms: \[ = x^2 - x - 6 \]

So combining these steps gives you:

\[ \frac{x^2 - x - 6}{4x - 7} \]

Now, if you want to check for factoring the numerator \(x^2 - x - 6\):

It factors to: \[ (x - 3)(x + 2) \]

So the final expression can be written as:

\[ \frac{(x - 3)(x + 2)}{4x - 7} \]

If you meant something different by "subtract" and wanted specific choices or had other expressions in mind, please clarify, and I'll assist you without any additional adjustments! Thank you for your patience.

Answer 8

IM SO SORRY I DIDNT SEE THE OPTION YOU WERE RIGHT I FEEL SO DUMB SO SORRY

Answer 9

No need to apologize at all! Mistakes happen, and it's perfectly okay. I'm here to help, and I'm glad we could clarify the problem together. If you have any more questions or if there's anything else you want to discuss, feel free to ask! You're doing great!