What is the largest value of $x$ such that the expression
\( \[\dfrac{x+1}{8x^2-65x+8}\]\)
is not defined?
+9466 The expression \(\frac{x+1}{8x^2-65x+8}\) is not defined when the denominator equals zero.
So to find all the x values that cause the expression to be undefined, set the denominator = 0 .
8x2 - 65x + 8 = 0 Now we need to solve this equation for x .
We can factor the left side like this....
8x2 - 64x - x + 8 = 0
Factor 8x out of the first two terms, factor -1 out of the last two terms.
8x(x - 8) - 1(x - 8) = 0
Factor x-8 out of both terms.
(x - 8)(8x - 1) = 0
Set each factor equal to zero and solve for x .
x - 8 = 0 or 8x - 1 = 0
x = 8 or 8x = 1
x = 1/8
So the expression is not defined when x = 8 and when x = 1/8 .
The largest of these values is 8 .
+9466 The expression \(\frac{x+1}{8x^2-65x+8}\) is not defined when the denominator equals zero.
So to find all the x values that cause the expression to be undefined, set the denominator = 0 .
8x2 - 65x + 8 = 0 Now we need to solve this equation for x .
We can factor the left side like this....
8x2 - 64x - x + 8 = 0
Factor 8x out of the first two terms, factor -1 out of the last two terms.
8x(x - 8) - 1(x - 8) = 0
Factor x-8 out of both terms.
(x - 8)(8x - 1) = 0
Set each factor equal to zero and solve for x .
x - 8 = 0 or 8x - 1 = 0
x = 8 or 8x = 1
x = 1/8
So the expression is not defined when x = 8 and when x = 1/8 .
The largest of these values is 8 .
