The non-permissible values for the expression -9x+8 divided by -9x^2-55x+56 are?
a) x does not equal -8/9
b)x does not equal 8
c) x does not equal 8/9 and x does not equal -7
d) there are no restrictions
hint:
-9x^2-55x+56 = (7+x)(8-9x)
To find the non-permissible values for the given expression, we need to identify the values of x that would make the denominator equal to zero. Division by zero is undefined in mathematics.
The denominator of the expression is -9x^2 - 55x + 56. To find its solutions, we can set it equal to zero and either factoring, completing the square, or using the quadratic formula.
-9x^2 - 55x + 56 = 0
We can now factor this quadratic equation:
(-9x + 7)(x + 8) = 0
Setting each factor equal to zero:
-9x + 7 = 0 or x + 8 = 0
Solving each equation individually:
-9x = -7 or x = -8
Dividing both sides by -9:
x = 7/9 or x = -8
So, the non-permissible values for the expression are x = 7/9 and x = -8.
Among the given options, the correct answer is c) x does not equal 8/9 and x does not equal -7, as these are the correct non-permissible values for the expression.