Equations with Fractions Involving Binomial Denominator

Worked Example 9.3.1:

Solution

i. \( \frac{1}{x\: +\: 3} \:+\: \frac{5}{1}\scriptsize = 0 \)

Find the L.C.M

\( \frac{1(1) \: + \:5(x \: + \:3)}{x \:+ \: 3} \scriptsize = 0 \)

\( \frac{1 \:+ \:5x \: + \:15}{x \: + \: 3} \scriptsize = 0 \)

Cross multiply

\( \scriptsize 1 \; + \; 5x \; + \; 15 = 0 \)

Take like terms

\( \scriptsize 5x \: + \: 16 \: = 0 \)

\( \scriptsize 5x = -16 \)

Divide both sides by 5

\( \frac{5x}{5} = \frac{-16}{5} \)

\( \frac{\not{5}x}{\not{5}} = \frac{-16}{5} \)

\( \scriptsize x = \normalsize \frac{-16}{5} \)

⇒ \( \scriptsize x = \scriptsize -3\frac{1}{5} \)

ii. \( \frac{10}{x \: - \: 2} \scriptsize = 4 \)

\( \scriptsize 10 = 4(x \: - \: 2)\)

\( \scriptsize 10 = 4x \: - \: 8\)

Take like terms

\( \scriptsize 10 \: + \: 8 \: = \: 4x \)

\( \scriptsize 18 = 4x \)

\( \scriptsize 4x =18 \)

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