Clear the equation of fractions by multiplying each term by the L. C. M. of the denominators,

6x+4x= 3x+420.

Transpose the unknown quantities and combine,

7x= 420.

Divide both numbers by 7, and we have

x = 60.

Substituting the value of x in the equation, we have

Multiplying each term by 75, the L. C. M. of the given denominators, we have

45x+150 — (150 x − 375) = 36 x + 45 ·

Removing parenthesis,

45x.

45x+150 150 x + 375 = 36 x + 45 — 45 x.

Transposing,

45 x 150 x − 36 x + 45 x 45 – 150 — 375.

Combining,

Dividing by 96,

=

175. If the numerator of a fraction is a polynomial, and the sign of the fraction negative, it will be found convenient on removing the denominator to enclose the numerator in a parenthesis; if this is not done, each sign of the numerator should be changed.

176. Hence, to solve a simple fractional equation:

Clear the equation of fractions by multiplying each term by the L. C. M. of the denominators; transpose the unknown terms to the first member, and the known terms to the second member of the equation; unite the similar terms, and divide by the coefficient of the unknown quantity.

177. A Literal Equation is one in which some or all of the known members are represented by letters.

Clear of fractions by multiplying each term by a2 - b2,