Question

Select the correct answer from each drop-down menu. The quotient of has x²+x−6/x²−6x+5 divided by x²+2x−3/x²−7x+10 in the numerator and in the denominator.

a. (x²+x−6)/(x²−6x+5)
b. (x²+2x−3)/(x²−7x+10)
c. (x²+x−6)/(x²+2x−3)
d. Not Mentioned

Answer 1

The student's question involves simplifying a complex algebraic fraction by inverting and multiplying fractions and then simplifying by factoring and canceling common terms.

Step-by-step explanation:

The question requires us to simplify a complex fractional expression in algebra. We have a fraction divided by another fraction in the numerator and a denominator. To simplify this, we need to invert the denominator and multiply it by the numerator. This process is a division of fractions and is similar to working with numeric fractions. However, it also involves algebraic expressions, which means we will factor and simplify whenever possible to obtain the simplest form of the expression.

If we denote the original expression as:

(x²+x−6)/(x²−6x+5) divided by (x²+2x−3)/(x²−7x+10),

first we invert the second fraction and convert the division into multiplication:

((x²+x−6)/(x²−6x+5)) × ((x²−7x+10)/(x²+2x−3)).

Next, we would factor each quadratic expression if possible, combining like terms, and then simplify the resulting expression by canceling out the common factors in the numerator and denominator.

The correct result depends on the actual factoring of the given quadratic expressions and the simplification of the overall expression.