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 :-
$\frac{ {x}^{2} + 11x + 28}{ {x}^{2} - 4x - 77} \div \frac{ {x}^{2} + 7x + 12 }{ {x}^{2} - 2x - 15 } \\ \frac{ {x}^{2} + 7x + 4x + 28}{ {x}^{2} - 11x + 7x - 77} \div \frac{ {x}^{2} + 4x + 3x + 12 }{ {x}^{2} - 5x + 3x - 15} \\ \frac{x(x + 7) + 4(x + 7)}{x(x - 11) + 7(x - 11)} \div \frac{x(x + 4) + 3(x + 4)}{x(x - 5) + 3(x - 5)} \\ \frac{(x + 7)(x + 4)}{(x - 11)(x + 7)} \times \frac{(x - 5)(x + 3)}{(x + 4)(x + 3)} \\ \frac{(x - 5)}{(x - 11)} ans$
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