Question

find x+3/x+1 and x+2/x+4

Answer 1

Hey there!

By factorisation method for this equation;

$\bf{\dfrac{x + 3}{x + 1} + \dfrac{x + 2}{x + 4}}$

Taking LCM and adjusting the fractions based on LCM:

$\bf{\dfrac{(x + 3)(x + 4)}{(x + 1)(x + 4)} + \dfrac{(x + 2)(x + 1)}{(x + 4)(x + 1)}}$

Because of equal denominators we can multiply the given fractions that is;

$\boxed{\bf{\dfrac{a}{b} +- \dfrac{b}{c} = \dfrac{a +- b}{c}}}$

Therefore,

$\bf{\dfrac{(x + 3)(x + 4) + (x + 2)(x + 1)}{(x + 1)(x + 4)}}$

$\bf{\dfrac{(xx + 4x + 3x + 3 \times 4) + (xx + 1 \times x + 2x + 2 \times 1)}{(x + 1)(x +4)}}$

$\bf{\dfrac{(x^2 + 7x + 12) + (x^2 + 3x + 2)}{(x + 1)(x + 4)}}$

$\boxed{\bf{\underline{\therefore \quad Final \: \: Factorised \: \: equation \: \: is = \dfrac{2x^2 + 10x + 14}{(x + 1)(x + 4)}}}}$

Which is the required factorisation for this type of query.

Hope this helps you and clears the doubts for factorising the whole values to get the final values!!!!!