4 years ago

Find the next four terms of the arithmetic sequence 11,15,19...

1 answer:

6 0

Each new term of this arith. seq. is obtained by adding 4 to the previous term. Hence, 15 = 11+4; 19=15+4, and so on. Add 4 to 19 to get the next term. Keep going until you have 4 new terms for the arith. seq. 11, 15, 19, .....

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What is the simplified form of 3/4x+3+21/8x^2-14x-15

creativ13 [48]

Solution:

We have been asked to find the simplified expression of

$3/4x+3+21/8x^2-14x-15=\frac{3}{4x+3} +\frac{21}{8x^2-14x-15}\\ \\ \text{We will have to make the denominator equal to add}\\ \\ \ 8x^2-14x-15=8x^2+6x-20x-15\\ \\ \ =2x(4x+3)-5(4x+3)=(4x+3)(2x-5)\\ \\ \frac{3}{4x+3} +\frac{21}{8x^2-14x-15}=\frac{3}{4x+3} +\frac{21}{(4x+3)(2x-5)}\\ \\ =\frac{3(2x-5)+21}{(4x+3)(2x-5)}\\ \\ =\frac{6x-15+21}{(4x+3)(2x-5)} \\ \\ =\frac{6x+6}{(4x+3)(2x-5)} \\$