Question

2. Divide the following and write your answer in lowest terms

Answer 1

SOLUTION IS IN THE ATTACHMENT

RATIONAL EXPRESSIONS :
A rational number is defined as a quotient a/b, of two integers a and b and b ≠0.A rational expression is a quotient p(x) /q(x) of two Polynomials p(x) and q(x) ,where q(x) ≠0.
•When the numerator and denominator of a rational expression do not have any common factor except 1, the rational expression is said to be expressed in the lowest terms.
•To reduce a rational expression to the lowest terms, factorise the numerator and the denominator and cancel the factors which are common to both.
•DIVISION OF RATIONAL EXPRESSIONS : p(x)/q(x) ÷ g(x)/h(x) = p(x)/q(x) × h(x)/g(x)

HOPE THIS WILL HELP YOU….

Answer 2

Solution:-

given by:-
$\frac{ 2{x}^{2} + 5x - 3}{2 {x}^{2} + 9x + 9 } \div \frac{2 {x}^{2} + x - 1 }{2 {x}^{2} + x - 3 } \\ \frac{2 {x}^{2} + 6x - x - 3}{2 {x}^{2} + 6x + 3x + 9 } \div \frac{2 {x}^{2} + 2x - x - 1}{ 2{x}^{2} + 3x - 2x - 3 } \\ \frac{2x(x + 3) - 1(x + 3)}{2x(x + 3) + 3(x + 3)} \div \frac{2x(x + 1) - 1(x + 1)}{x(2x + 3) -1(2x + 3) } \\ \frac{(x + 3)(2x - 1)}{(x + 3)(2x + 3)} \times \frac{(2x + 3)(x - 1)}{(x + 1)(2x - 1)} \\ \frac{(x - 1)}{(x + 1)} ans$
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