Quantum Physics

A.3 Algebra A.3by 8, we have8x8 32 8x 4Next consider the equationx 2 8In this type of expression, we can add or subtract the same quantity from eachside. If we subtract 2 from each side, we getIn general, if x a b, then x b a.Now consider the equationx 2 2 8 2x 6x5 9If we multiply each side by 5, we are left with x on the left by itself and 45 on theright: x 5 (5) 9 5x 45In all cases, whatever operation is performed on the left side of the equality mustalso be performed on the right side.The following rules for multiplying, dividing, adding, and subtracting fractionsshould be recalled, where a, b, and c are three numbers:RuleExampleMultiplyingDividingAdding a b c d acbd(a/b)(c/d) adbcab c dad bcbd 2 3 4 5 8152/34/5 (2)(5)(4)(3) 101223 4 5(2)(5) (4)(3)(3)(5) 215EXERCISESIn the following exercises, solve for x:ANSWERS1.2.3.4.a 11 x3x 5 13ax 5 bx 252x 6 34x 8x 1 aax 6x 7a bx 11 7B. PowersWhen powers of a given quantity x are multiplied, the following rule applies:x n x m x nmFor example, x 2 x 4 x 24 x 6 .[A.3]