Homework

# math

a) Simplify: 1/x + 1/x-1             b)...
a) Simplify: 1/x + 1/x-1
b) Solve: 1/x +1/x-1 = 0
c) When solving a rational equation in part b), why it is OK to remove the denominator by multiplying both sides by LCD and why can you not do the same operation when simplifying a rational expression in a) above.
d) Use discriminant to discuss the number of solutions of the following quadratic equations:
a)    x^2-x-1=0 ;        b)   2x^2-8x=-8

e) What are the different types of equations you have learned to solve? Describe and give examples.
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4/5/2005
xarqi, Generalist
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a)
1/x + 1/(x-1) = (x - 1)/x(x - 1) + x/x(x - 1)
= (2x - 1)/x(x - 1) [Hmm - is that much simpler?]

b) From above:
(2x - 1)/x(x - 1) = 0
=> 2x - 1 = 0, x not equal to 0, x not equal to 1
=> 2x = 1
=> x = 1/2

c)Because in (a), not all terms have the LCD as denominator.

d)(a) b^2 - 4ac = 5. Therefore 2 solutions
(b) b^2 - 4ac = 0. Therefore 1 solution.

e) I'm not sure what they all are. I've just seen rational

A rational polynomial can be expressed as the quotient of two
polynomials, for example (2x + 1)/(x^2 - 1) = 0

A quadratic is a polynomial in one variable of order 2, for
example: x^2 + 2x + 4 = 0
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