Please help me solve and find the excluded values for this problem. Also please show me the work for this problem I want to learn!@!@!. 49X^6+7X^7/28X^8
I have a feeling you meant:
(49X^6+7X^7)/(28X^8)
take out a common factor
= 7x^6( 7 + x)/(28x^8)
now divide
= (7+x)/(4x^2)
now we divided top and bottom by a variable. If that variable is zero, we just divided by zero, which is a mathematical no-no.
so we have to state a restriction of x ≠ 0
(49X^6+7X^7)/(28X^8)
= (x+7)/(4x^2) , x ≠ 0
To solve the expression 49X^6 + 7X^7 / 28X^8, let's break it down step by step:
Step 1: Simplify the expression within the parentheses.
49X^6 + 7X^7 / 28X^8 simplifies to 49X^6 + (7X^7 / 28X^8).
Step 2: Simplify the fraction.
To simplify the fraction, let's first simplify the numerator and denominator separately:
Numerator: 7X^7
Denominator: 28X^8
Step 3: Simplify the numerator.
The numerator, 7X^7, cannot be further simplified since there are no common factors other than 1.
Step 4: Simplify the denominator.
To simplify the denominator, 28X^8, we can factor out the common factors 4 and X^8:
28X^8 = 4 * 7 * X^8 = 4 * 7X^8.
Step 5: Rewrite the expression.
Now that we have simplified the numerator and denominator, we can rewrite the expression:
49X^6 + (7X^7 / 28X^8) = 49X^6 + 7X^7 / 4 * 7X^8.
Step 6: Simplify the expression.
Now we can simplify the expression further by canceling out common factors between the numerator and denominator:
49X^6 + 7X^7 / 4 * 7X^8 = 49X^6 + X^7 / 4X.
Therefore, the simplified expression is 49X^6 + X^7 / 4X.
To find the excluded values, we need to identify any values of X that would make the denominator, 4X, equal to zero. In this case, the denominator can equal zero when X is equal to zero: X = 0.
Hence, the excluded value for this expression is X = 0.