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Explain Simplifying Rational Expressions ?
A rational expression, or algebraic fraction, is an expression in which you have a polynomial divided by a polynomial. Sometimes it is said that a rational expression is a polynomial "over" a polynomial.
Here are two examples of rational expressions:
10x3y/15x2y4 and (2x2 +11x +15) /x2-9
Important: The bottom polynomial can never be zero, because division by zero is undefined!To simplify or reduce a fraction such as 6/15, you must first factor the numerator and denominator, and then you can eliminate, or cross out, the common factors.
Like this:
The same canceling procedure can be used to simplify rational expressions. Here are some examples of how you can do this:
There actually isn't a whole lot to do throughout this case. We'll find two solutions which will form a basic set of solutions and therefore our general solution will be as,
Question: Solve the initial value problem 2x'' +x'-x =27 Cos2t +6 Sin 2t, x(0)=2 , x'(0)= -2 by using Laplace transform method.
How would you solve this question? 4/5 = 8/x+2
Prove that three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the medians of the triangle. Ans: To prove 3(AB 2
4.2^2x+1-9.2^x+1=0
A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.
Two circles touch externally. The sum of their areas is 58 π cm 2 and the distance between their centres is 10 cm. Find the radii of the two circles. (Ans:7cm, 3cm) Ans:
3/45
A dealer sells a toy for Rs.24 and gains as much percent as the cost price of the toy. Find the cost price of the toy. Ans: Let the C.P be x ∴Gain = x % ⇒ Gain = x
Question 1 Explain Peano's Axioms with suitable example Question 2 Let A = B = C= R, and let f: A→ B, g: B→ C be defined by f(a) = a+1 and g(b) = b 2 +1. Find a) (f °g
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