To divide two fractions, we invert the second fraction and multiply.
\frac{6-x}{x^2+2x-3} \div \frac{x^2-4x-12}{x^2+4x+3}
Inverting the second fraction:
\frac{6-x}{x^2+2x-3} \cdot \frac{x^2+4x+3}{x^2-4x-12}
Factor the polynomials:
\frac{6-x}{(x-1)(x+3)} \cdot \frac{(x+3)(x+1)}{(x-6)(x+2)}
Divide by multiplying the reciprocal:
\frac{(6-x)(x+3)(x+1)}{(x-1)(x+3)(x-6)(x+2)}
Canceling out the common factors:
\frac{-(x-6)(x+1)}{(x-6)(x+2)}
Simplify:
\frac{-x+6}{x+2}
Therefore, the quotient in simplified form is \frac{-x+6}{x+2}.
Restrictions on the variable are:
1. x cannot equal 1, -3, -2, or 6 because these values make the denominator(s) zero.
What is the quotient \frac{6-x}{x^2+2x-3}\div\frac{x^2-4x-12}{x^2+4x+3} in simplified form? State any restrictions on the variable.
1 answer