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Adding Rational Expressions with Common Denominators
To add or subtract fractions or rational expressions with common denominators, all you do is add or subtract the numerators. You then write the sum or difference over the common denominator, and simplify.
Here are some fractional examples that should be familiar to you:
5/8 + 1/8 = (5+1)/8 9/16 -7/16 = (9-7)/16
= 6/8 = 2/16
= 3/4 =1/8
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If cos?+sin? = √2 cos?, prove that cos? - sin? = √2 sin ?. Ans: Cos? + Sin? = √2 Cos? ⇒ ( Cos? + Sin?) 2 = 2Cos 2 ? ⇒ Cos 2 ? + Sin 2 ?+2Cos? Sin? = 2Cos 2 ? ⇒
The digraph D for a relation R on V = {1, 2, 3, 4} is shown below (a) show that (V,R) is a poset. (b) Draw its Hasse diagram. (c) Give a total order that have R.
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