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.