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algebra intermediate

Problem

When

x

is added to both the numerator and denominator of the fraction

\frac{a}{b}, a \neq = b, b \neq = 0

, the value of the fraction is changed to

\frac{c}{d}

. Then

x

equals:

(A)

\frac{1}{c - d}

(B)

\frac{a d - b c}{c - d}

(C)

\frac{a d - b c}{c + d}

(D)

\frac{b c - a d}{c - d}

Solution

\frac{a + x}{b + x} = \frac{c}{d}

,

b c + c x = a d + d x

,

(c - d) x = a d - b c

,

x = \frac{a d - b c}{c - d}

. The answer is

\frac{a d - b c}{c - d}

.

Final answer

B