Multiply by 33, the L. C. M. of the denominators.

NOTE. Since the minus sign precedes the second fraction, in removing the denominator the sign of every term of the numerator

174. To Clear an Equation of Fractions, therefore, Multiply each term by the L. C. M. of the denominators.

If a fraction is preceded by a minus sign, the sign of every term of the numerator must be changed when the denominator is removed.

NOTE.

The solution of this and similar problems will be much easier by combining the fractions on the left side and the fractions on the right side than by the rule.

Since the numerators are equal, the denominators are equal.
Hence, (x-5) (x − 6) = (x — 8) (x — 9).

Solving, we have

x = 7.

175. If the denominators contain both simple and compound expressions, it is best to remove the simple expressions first, and then each compound expression in turn. After each multiplication the result should be reduced to the simplest form.

Simplify the complex fractions by multiplying both terms of each fraction by 9.

176. Literal equations are equations in which some or all of the given numbers are represented by letters; known numbers are represented by the first letters of the alphabet.