Simplify each expression and state any non-permissible values. (4 marks - show your work)
4x-1/x^2+7x+12 divided by 2x-1/x^2+x-12
My work on simplifying the expressions:
4x-1/(x+3)(x+4)divided by 2x-1/(x+4)(x-3)
If I've gone wrong please help me understand where I went wrong and help me get the correct answer.
Sincerely, yours
Alex Hunter
(4x-1)/[(x+3)(x+4)] * (x+4)(x-3)/(2x-1)
when you divide fractions, invert the denominator and multiply
(x+4) cancels
(4x-1)(x-3) /[ (x+3)(2x-1)]
The given expression is:
(4x-1)/(x^2+7x+12) ÷ (2x-1)/(x^2+x-12)
To simplify this expression, we need to follow the order of operations (PEMDAS/BODMAS).
Step 1: Factor both denominators.
The factors of x^2+7x+12 are (x+3)(x+4).
The factors of x^2+x-12 are (x+4)(x-3).
Step 2: Rewrite the expression using the factors.
(4x-1)/[(x+3)(x+4)] ÷ (2x-1)/[(x+4)(x-3)]
Step 3: Invert the second fraction and change the division sign to multiplication.
(4x-1)/[(x+3)(x+4)] × [(x+4)(x-3)]/(2x-1)
Step 4: Simplify by canceling out common factors.
We can cancel out (x+4) in both the numerator and denominator:
(4x-1)/[(x+3)] × [(x-3)]/(2x-1)
Now, let's combine the numerators and denominators:
[(4x-1)(x-3)] / [(x+3)(2x-1)]
Expanding the numerator:
(4x^2 - 13x + 3) / [(x+3)(2x-1)]
Therefore, the simplified expression is:
(4x^2 - 13x + 3) / [(x+3)(2x-1)]
To find the non-permissible values, we need to identify the values of x that would make the denominator zero. In this case, the non-permissible values occur when the denominator (x+3)(2x-1) equals zero.
Setting each factor equal to zero gives us:
x+3 = 0 --> x = -3
2x-1 = 0 --> x = 1/2
Therefore, the non-permissible values are x = -3 and x = 1/2. These values should be excluded from the domain of the expression.