Simplify each expression and state any non-permissible values. ( 3 marks - show your work)
x/(x^2-3x-4)-4/(x+1)
Please help me!
x^2-3x-4 = (x-4)(x+1)
So, you have
x/[(x-4)(x+1)] - 4/(x+1)
(x - 4(x-4))/[(x-4)(x+1)]
(16-3x)/[(x-4)(x+1)]
As usual, you cannot divide by zero, so any values of x that make a denominator zero are excluded.
Now show us what you got on the others you posted. As it says, show your work.
To simplify the expression, we need to combine the fractions into one.
First, let's find the common denominator. The common denominator is the product of the denominators of the two fractions, which is (x^2-3x-4)(x+1).
Next, we need to convert each fraction to have the common denominator. For the first fraction, multiply the numerator and denominator by (x+1), and for the second fraction, multiply the numerator and denominator by (x^2-3x-4).
After multiplying, the expression becomes:
x(x+1)/(x^2-3x-4)(x+1) - 4(x^2-3x-4)/(x^2-3x-4)(x+1)
Now, we can combine the fractions:
[x(x+1) - 4(x^2-3x-4)] / (x^2-3x-4)(x+1)
Next, let's simplify the numerator:
[x^2 + x - (4x^2 - 12x - 16)] / (x^2-3x-4)(x+1)
Now, distribute the negative sign to the terms inside the parentheses:
[x^2 + x - 4x^2 + 12x + 16] / (x^2-3x-4)(x+1)
Combine like terms in the numerator:
(-3x^2 + 13x + 16) / (x^2-3x-4)(x+1)
Lastly, we need to check for any non-permissible values. Non-permissible values are values of x that would make the denominator zero since division by zero is undefined.
For this expression, the non-permissible values are the solutions to the quadratic equation x^2 - 3x - 4 = 0 and the x + 1 = 0 equation.
Let's solve for x:
Using factoring or the quadratic formula, x^2 - 3x - 4 = 0 can be factored as (x - 4)(x + 1) = 0. So the solutions are x = 4 and x = -1.
For x + 1 = 0, the solution is x = -1.
Therefore, the non-permissible value for this expression is x = -1.
To summarize:
The simplified expression is (-3x^2 + 13x + 16) / (x^2 - 3x - 4)(x + 1) and the non-permissible value is x = -1.