X.

10. $(a+bx)(c+d)=(a+b)(c+dx)$.

11. ${\displaystyle \frac{x}{a-b}}-{\displaystyle \frac{3a}{a+b}}={\displaystyle \frac{bx}{a^2-b^2}}$.

142. Problems involving Fractional Equations.

Exercise 55.

Ex. The sum of the third and fifth parts of a certain number exceeds two times the difference of the fourth and sixth parts by $22$. Find the number.

lint Let x = the number. lint Then x3 + x5 = the sum of its third and fifth parts, x4 - x6 = the difference of its fourth and sixth parts, 2(x4 - x6) = $2$ times the difference of fourth and sixth parts,

x3 + x5 - 2(x4 - x6) = the given excess. lint But 22 = the given excess. x3 + x5 - 2(x4 - x6) = 22.

Multiply by $60$ the L. C. D. of the fractions.

The required number, therefore, is $60$.

1. The difference between the fifth and seventh parts of a certain number is $2$. Find the number.

2. One-half of a certain number exceeds the sum of its fifth and seventh parts by $11$. Find the number.

3. The sum of the third and