Browse · harp

smc

algebra intermediate

Problem

The expression

\frac{x ^{2} - 3 x + 2}{x ^{2} - 5 x + 6} \div \frac{x ^{2} - 5 x + 4}{x ^{2} - 7 x + 12},

when simplified is:

(A)

f r a c ((x - 1) (x - 6), (x - 3) (x - 4))

(B)

\frac{x + 3}{x - 3}

(C)

\frac{x + 1}{x - 1}

(D)

1

Solution

Factoring each of the binomials in the expression

\frac{x ^{2} - 3 x + 2}{x ^{2} - 5 x + 6} \div \frac{x ^{2} - 5 x + 4}{x ^{2} - 7 x + 12},

will yield the result of

\frac{( x - 2 ) ( x - 1 )}{( x - 3 ) ( x - 2 )} \div \frac{( x - 4 ) ( x - 1 )}{( x - 3 ) ( x - 4 )},

We can eliminate like terms to get

\frac{x - 1}{x - 3} \div \frac{x - 1}{x - 3}

, which, according to identity property, is equivalent to the answer

1

.

Final answer

D