Question

1. Multiply 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.
•MULTIPLICATION OF RATIONAL EXPRESSIONS : p(x)/q(x) × g(x)/h(x)

HOPE THIS WILL HELP YOU….

Answer 2

Solution:-

given by:-
$\frac{3 {x}^{2} + 2x - 1}{ {x}^{2} - x - 2} \times \frac{2 {x}^{2} - 3x - 2}{3 {x}^{2} + 5x - 2} \\ \frac{3 {x}^{2} + 3x - x - 1 }{ {x}^{2} - 2x + x - 2 } \times \frac{2 {x}^{2} - 4x + x - 2}{3 {x}^{2} + 6x - x - 2 } \\ \frac{3x(x + 1) - 1(x + 1)}{ x( x - 2) + 1(x - 2) } \times \frac{2x(x - 2) + 1(x - 2)}{3x(x + 2) - 1(x + 2)} \\ \frac{(x + 1)(3x - 1)}{(x - 2)(x + 1)} \times \frac{(x - 2)(2x + 1)}{(x + 2)(3x - 1)} \\ \frac{2x + 1}{x + 2}$
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