Simplify. x/(7x+x^2)

• 1/(7+x); where x ≠-7
• 1/(7x); where x≠0
• 1/(7+x); where x≠0,-7
• 1/7

How?

7x+x^2 = x(7+x)

divide and cancel the x factor, leaving

1/(x+7)

But, you cannot divide by zero, so x = -7 is excluded.

You also cannot simply cancel the x factors, if x=0.

So, (C)

To simplify the expression x/(7x + x^2), we can factor out an x from the denominator.

Step 1: Factor out an x from the denominator:
x/(x(7 + x))

Step 2: Cancel out the x in the numerator with the x in the denominator:
1/(7 + x)

So, the simplified expression is 1/(7 + x). However, there are some restrictions for the value of x to avoid dividing by zero or having undefined expressions.

Restrictions:
- x cannot be equal to 0 because it would result in division by zero.
- x cannot be equal to -7 because it would result in undefined expression.

Therefore, the simplified expression is 1/(7 + x), where x ≠ 0 and x ≠ -7.

To simplify the expression x/(7x+x^2), we can factor out an x from the denominator.

Step 1: Factor out x from the denominator:
x/(x(7+x))

Step 2: Cancel out the common factors:
1/(7+x)

Therefore, the simplified expression is 1/(7+x), where x ≠ 0.