A (-2x+17)/(2x(x-4)) B (2x-23)/(2(x-4)) C D (4x-46)/(2x(x-4)) 7. Simplify (x^2-3x-4)/(x^2)+x-6div (x^2+4x+3)/(x^2)-9 A ((x-2)(x+3)(x-3))/((x-4)(x+1)^2) ((x+2)(x-3))/((x+4)(x+3)) ((x-2)(x+3))/((x-4)(x-3)) (x-4)(x-3) D ((x-4)(x-3))/((x-2)(x+3)) 8. Find the product: (x^2+6x-16)/(x-8)cdot (x+2)/(x^2)-4 A ((x+6)(x-2)(x+2))/(x(x-8)(x-4)) B ((x-6))/((x+8)) C ((x+8))/((x-8)) D ((x+6))/((x-8)) 9. Find the quotient: (x^2-3x-10)/(4x(x-1))div (x-5)/(x^2)-x A ((x-2)(x-3))/(2x(x-1)) B ((x-2)(x-3))/((x-1)) C ((x+2))/(4) D (4x(x-1))/((x-5)) Simplify (6x-8)/(4x(x-10))-(6)/(4x) (11)/((-2)) B (13)/(x(x-10)) C (19)/(4x(x-10)) D (6x)/(2x(x-5))

7. Simplify<br />$\frac {x^{2}-3x-4}{x^{2}+x-6}\div \frac {x^{2}+4x+3}{x^{2}-9}$<br />A $\frac {(x-2)(x+3)(x-3)}{(x-4)(x+1)^{2}}$<br />$\frac {(x+2)(x-3)}{(x+4)(x+3)}$<br />$\frac {(x-2)(x+3)}{(x-4)(x-3)}$<br />(x-4)(x-3)<br />D<br />$\frac {(x-4)(x-3)}{(x-2)(x+3)}$<br /><br />To simplify the given expression, we can first factorize the numerator and denominator of each fraction:<br /><br />$\frac {x^{2}-3x-4}{x^{2}+x-6}\div \frac {x^{2}+4x+3}{x^{2}-9}$<br /><br />Factorizing the numerator and denominator of the first fraction:<br />$x^{2}-3x-4 = (x-4)(x+1)$<br />$x^{2}+x-6 = (x-2)(x+3)$<br /><br />Factorizing the numerator and denominator of the second fraction:<br />$x^{2}+4x+3 = (x+1)(x+3)$<br />$x^{2}-9 = (x-3)(x+3)$<br /><br />Now, we can rewrite the expression as:<br />$\frac {(x-4)(x+1)}{(x-2)(x+3)}\div \frac {(x+1)(x+3)}{(x-3)(x+3)}$<br /><br />To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:<br />$\frac {(x-4)(x+1)}{(x-2)(x+3)}\times \frac {(x-3)(x+3)}{(x+1)(x+3)}$<br /><br />Simplifying the expression:<br />$\frac {(x-4)(x-3)}{(x-2)(x+3)}$<br /><br />Therefore, the correct answer is D) $\frac {(x-4)(x-3)}{(x-2)(x+3)}$.<br /><br />8. Find the product: $\frac {x^{2}+6x-16}{x-8}\cdot \frac {x+2}{x^{2}-4}$<br />A $\frac {(x+6)(x-2)(x+2)}{x(x-8)(x-4)}$<br />B $\frac {(x-6)}{(x+8)}$<br />C $\frac {(x+8)}{(x-8)}$<br />D $\frac {(x+6)}{(x-8)}$<br /><br />To find the product, we can multiply the numerators and denominators of the two fractions:<br /><br />$\frac {x^{2}+6x-16}{x-8}\cdot \frac {x+2}{x^{2}-4}$<br /><br />Multiplying the numerators:<br />$(x^{2}+6x-16)(x+2) = x^{3}+8x^{2}+4x-32$<br /><br />Multiplying the denominators:<br />$(x-8)(x^{2}-4) = x^{3}-12x+32$<br /><br />Therefore, the product is:<br />$\frac {x^{3}+8x^{2}+4x-32}{x^{3}-12x+32}$<br /><br />Simplifying the expression:<br />$\frac {(x+8)(x-2)(x+2)}{(x-8)(x-4)(x+4)}$<br /><br />Therefore, the correct answer is A) $\frac {(x+8)(x-2)(x+2)}{x(x-8)(x-4)}$.<br /><br />9. Find the quotient:<br />$\frac {x^{2}-3x-10}{4x(x-1)}\div \frac {x-5}{x^{2}-x}$<br />A $\frac {(x-2)(x-3)}{2x(x-1)}$<br />B<br />$\frac {(x-2)(x-3)}{(x-1)}$<br />C $\frac {(x+2)}{4}$<br />D<br />$\frac {4x(x-1)}{(x-5)}$<br /><br />To find the quotient, we can multiply the first fraction by the reciprocal of the second fraction:<br /><br />$\frac {x^{2}-3x-10}{4x(x-1)}\times \frac {x^{2}-x}{x-5}$<br /><br />Simplifying the expression:<br />$\frac {(x^{2}-3x-10)(x^{2}-x)}{4x(x-1)(x-5)}$<br /><br />Therefore, the correct answer is D) $\frac {4x(x-1)}{(x-5)}$