Question
Divide x over x+3 divided by x over x-4
Answers
GPT-4o mini
To divide the expression \(\frac{x}{x+3}\) by \(\frac{x}{x-4}\), you can follow these steps:
1. **Write the division as a multiplication by the reciprocal**:
\[
\frac{x}{x+3} \div \frac{x}{x-4} = \frac{x}{x+3} \times \frac{x-4}{x}
\]
2. **Multiply the fractions**:
\[
\frac{x \cdot (x-4)}{(x+3) \cdot x}
\]
3. **Cancel out the common factors** (if \(x \neq 0\)):
\[
\frac{x-4}{x+3}
\]
So the simplified result is:
\[
\frac{x-4}{x+3}
\]
This assumes \(x \neq 0\), \(x \neq -3\), and \(x \neq 4\) to avoid division by zero.
1. **Write the division as a multiplication by the reciprocal**:
\[
\frac{x}{x+3} \div \frac{x}{x-4} = \frac{x}{x+3} \times \frac{x-4}{x}
\]
2. **Multiply the fractions**:
\[
\frac{x \cdot (x-4)}{(x+3) \cdot x}
\]
3. **Cancel out the common factors** (if \(x \neq 0\)):
\[
\frac{x-4}{x+3}
\]
So the simplified result is:
\[
\frac{x-4}{x+3}
\]
This assumes \(x \neq 0\), \(x \neq -3\), and \(x \neq 4\) to avoid division by zero.
sayletyler
Ok bestie im gonna need you to size the explanation down for me thank you
GPT-4o mini
Sure! Here’s the concise version:
To divide \(\frac{x}{x+3}\) by \(\frac{x}{x-4}\):
1. Rewrite it as a multiplication:
\[
\frac{x}{x+3} \times \frac{x-4}{x}
\]
2. The \(x\) cancels out (assuming \(x \neq 0\)):
\[
\frac{x-4}{x+3}
\]
So, the answer is:
\[
\frac{x-4}{x+3}
\]
(Note: \(x \neq 0, -3, 4\) to avoid division by zero.)
To divide \(\frac{x}{x+3}\) by \(\frac{x}{x-4}\):
1. Rewrite it as a multiplication:
\[
\frac{x}{x+3} \times \frac{x-4}{x}
\]
2. The \(x\) cancels out (assuming \(x \neq 0\)):
\[
\frac{x-4}{x+3}
\]
So, the answer is:
\[
\frac{x-4}{x+3}
\]
(Note: \(x \neq 0, -3, 4\) to avoid division by zero.)
sayletyler
I need like 4 senteces at most please
GPT-4o mini
To divide \(\frac{x}{x+3}\) by \(\frac{x}{x-4}\), rewrite it as \(\frac{x}{x+3} \times \frac{x-4}{x}\). The \(x\) cancels out, giving you \(\frac{x-4}{x+3}\). The result is \(\frac{x-4}{x+3}\), assuming \(x \neq 0, -3, 4\).
sayletyler
subract x over x+1 minus 8 over x-7
GPT-4o mini
To subtract \(\frac{x}{x+1}\) and \(\frac{8}{x-7}\), follow these steps:
1. Find a common denominator, which is \((x+1)(x-7)\).
2. Rewrite the fractions:
\[
\frac{x}{x+1} = \frac{x(x-7)}{(x+1)(x-7)}
\]
\[
\frac{8}{x-7} = \frac{8(x+1)}{(x+1)(x-7)}
\]
3. Now subtract:
\[
\frac{x(x-7) - 8(x+1)}{(x+1)(x-7)}
\]
4. Simplify the numerator:
\[
x^2 - 7x - 8x - 8 = x^2 - 15x - 8
\]
5. The final result is:
\[
\frac{x^2 - 15x - 8}{(x+1)(x-7)}
\]
So,
\[
\frac{x^2 - 15x - 8}{(x+1)(x-7)}
\] is the simplified result.
1. Find a common denominator, which is \((x+1)(x-7)\).
2. Rewrite the fractions:
\[
\frac{x}{x+1} = \frac{x(x-7)}{(x+1)(x-7)}
\]
\[
\frac{8}{x-7} = \frac{8(x+1)}{(x+1)(x-7)}
\]
3. Now subtract:
\[
\frac{x(x-7) - 8(x+1)}{(x+1)(x-7)}
\]
4. Simplify the numerator:
\[
x^2 - 7x - 8x - 8 = x^2 - 15x - 8
\]
5. The final result is:
\[
\frac{x^2 - 15x - 8}{(x+1)(x-7)}
\]
So,
\[
\frac{x^2 - 15x - 8}{(x+1)(x-7)}
\] is the simplified result.
sayletyler
2 things
1. I need the explantion trimmed down to like 4 sentences
2. can you do the expalnaton where any time theres fractions you say like how I said it in my question with saying x over x-1
Also can you not add any double parenthesis or {} these things or backwards slash
1. I need the explantion trimmed down to like 4 sentences
2. can you do the expalnaton where any time theres fractions you say like how I said it in my question with saying x over x-1
Also can you not add any double parenthesis or {} these things or backwards slash
GPT-4o mini
To subtract x over x+1 and 8 over x-7, find a common denominator, which is (x+1)(x-7). Rewrite the fractions as (x(x-7) over (x+1)(x-7)) and (8(x+1) over (x+1)(x-7)). Now subtract: (x(x-7) - 8(x+1)) over (x+1)(x-7). Simplifying gives you (x^2 - 15x - 8) over (x+1)(x-7).
sayletyler
I said remove the double parenthesis
GPT-4o mini
Got it! Here’s the explanation without double parentheses:
To subtract x over x+1 and 8 over x-7, find a common denominator, which is x+1 times x-7. Rewrite the fractions as x times (x-7) over that denominator and 8 times (x+1) over the same denominator. Now subtract: (x times (x-7) minus 8 times (x+1)) over x+1 times x-7. Simplifying gives you (x^2 - 15x - 8) over x+1 times x-7.
To subtract x over x+1 and 8 over x-7, find a common denominator, which is x+1 times x-7. Rewrite the fractions as x times (x-7) over that denominator and 8 times (x+1) over the same denominator. Now subtract: (x times (x-7) minus 8 times (x+1)) over x+1 times x-7. Simplifying gives you (x^2 - 15x - 8) over x+1 times x-7.
sayletyler
Bestie thats not an answer but theres one similar its
x^2-15x-8 over x^2-6x-7
x^2-15x-8 over x^2-6x-7
GPT-4o mini
I apologize for the confusion! Let's adjust the final expression accordingly:
To subtract x over x+1 and 8 over x-7, find a common denominator, which is x+1 times x-7. Rewrite the fractions as x times (x-7) over that denominator and 8 times (x+1) over the same denominator. Now subtract: (x times (x-7) minus 8 times (x+1)) over x+1 times x-7. Simplifying gives you (x^2 - 15x - 8) over (x^2 - 6x - 7).
To subtract x over x+1 and 8 over x-7, find a common denominator, which is x+1 times x-7. Rewrite the fractions as x times (x-7) over that denominator and 8 times (x+1) over the same denominator. Now subtract: (x times (x-7) minus 8 times (x+1)) over x+1 times x-7. Simplifying gives you (x^2 - 15x - 8) over (x^2 - 6x - 7).