We have then the following rule for clearing an equation of fractions: Multiply each term by the lowest common multiple of the denominators. Multiplying through by 20, the L.C.M. of 4, 5, and 10, - 15x-5-(16x-20)=80+ 14x+10 15x5 16x+20=80+14x+10 15x16x14x=80+ 10+ 5 — 20 x= 5, Ans. Note. If a fraction whose numerator is a polynomial is preceded by a - sign, care must be taken to change the sign of each term of the numerator when the denominator is removed. It is convenient, in such a case, to enclose the numerator in a parenthesis, as shown in the above example. 22. 1 (x+1) − Multiplying each term by x2-1, the L.C.M. of the denom inators, 2 (x + 1) − 3 (x − 1) − 1 = 0 2x+2-3x+3−1=0 2x-3x=-2-3+1 Multiplying by 7x-16, 28x-64 – 30 x — 60 = x=2, Ans. Note. If the denominators are partly monomial and partly polynomial, it is often advantageous to clear of fractions at first partially; multiplying by a quantity which will remove the monomial denomi 176. 1. Solve the equation 2 ax−3b=x+c — 3 ax. Transposing and uniting terms, 5 ax-x=3b+c. 2. Solve the equation (b — cx)2 — (a — cx)2 = b (b − a). Performing the operations indicated, b2 − 2 bcx + c2x2 − (a2 − 2 acx + c2x2 ) = b2 — ab b2 - 2 bcx + c2x2 - a2 + 2 acx — c2x2 = b2 — ab Factoring both members, 2 cx (a−b) = a(a - b) |