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Create an abstract image that symbolizes mathematical simplification and solution. The scene is dominated by a large quest for the truth, represented by a beacon of light shining through clouds onto a calculator. The background can be adorned with oversized fraction bars and algebraic x variables. No text should be included in the image.

Simplify 5x^3/7x^3+x^4

Is the answer 5/7+x where x is not equal to 0,-7?

Anyone got the answers for the test?

yes

but online, there is an implied order of operations, and parentheses are required to avoid ambiguity

5/7+x could be either
5/7 + x
or
5/(7+x) which is what you wanted.

In the absence of parens, multiplication and division are done before addition and subtraction., so 5/7+x is interpreted as (5/7)+x

Okay, thank you.

Why did the math book go to the comedy club? It wanted to practice its "times" tables and have a laugh at the same time! Now, let's dive into your question.

To simplify the expression 5x^3 / (7x^3 + x^4), we can first factor out the common term of x^3 in the denominator:

5x^3 / (x^3 * (7 + x))

Next, we can cancel out the common factor of x^3 in the numerator and denominator:

5 / (7 + x)

So, the simplified expression is 5 / (7 + x). You were right, but I couldn't resist adding a touch of humor! Just remember, this simplification is valid for any value of x, as long as it's not equal to 0 or -7.

To simplify the expression 5x^3 / (7x^3 + x^4), we can factor out the common term x^3 from the denominator:

5x^3 / (x^3 * (7 + x))

Next, we can simplify the expression further by canceling out the common factors:

5 / (7 + x)

So, the simplified expression is 5 / (7 + x).

However, it is important to note the condition in the given answer: "where x is not equal to 0 and -7." This is because when x is equal to 0 or -7, the denominator becomes zero, leading to an undefined expression. Therefore, the simplified expression 5 / (7 + x) is valid for all real numbers except 0 and -7.