Question

if (4/x+1)+(5/x+3)=(9/x+2) then find x please give the answer of this question with solution​

Answer 1

Answer:

4/x+1+5/x+3=9/x+2

4(x +3) (x+2) +5(x+1)(x+2) = 9(x+1)

(x+3)

4(x2+3x+2x +6) +5(x2+x+2x+2) =

9(x2+x +3x+3)

4x2 +20 x +24 +5x2+15x+10=

9x2+ 36x +27

= 9x2+35x+34 = 9x2+ 36x+27

x = 7. Ans

Answer 2

Answer :-

Value of x is 7.

Explanation :-

$\sf \dfrac{4}{x + 1} + \dfrac{5}{x + 3} = \dfrac{9}{x + 2} \\ \\ \\ \texttt{ \underline{taking lcm}} \\ \\ \\ \sf \implies \dfrac{4(x + 3) + 5(x + 1)}{(x + 1)(x + 3)} = \dfrac{9}{x + 2} \\ \\ \\ \sf \implies \dfrac{4x + 12 + 5x + 5}{x(x + 3) + 1(x + 3)} = \dfrac{9}{x + 2} \\ \\ \\ \sf \implies \dfrac{9x + 17}{ {x}^{2} + 3x + x + 3 } = \dfrac{9}{x + 2} \\ \\ \\ \sf \implies \dfrac{9x + 17}{ {x}^{2} + 4x + 3} = \dfrac{9}{x + 2}$

By cross multiplication

⇒ (9x + 17)(x + 2) = 9(x² + 4x + 3)

⇒ 9x(x + 2) + 17(x + 2) = 9x² + 36x + 27

⇒ 9x² + 18x + 17x + 34 = 9x² + 36x + 27

⇒ 9x² + 35x + 34 = 9x² + 36x + 27

⇒ 9x² + 35x + 34 - 9x² - 36x - 27 = 0

⇒ - x + 7 = 0

⇒ 7 = x

⇒ x = 7

Verification :-

$\sf \dfrac{4}{x + 1} + \dfrac{5}{x + 3} = \dfrac{9}{x + 2} \\ \\ \\ \sf \implies \dfrac{4}{7 + 1} + \dfrac{5}{7 + 3} = \dfrac{9}{7 + 2} \\ \\ \\ \sf \implies \dfrac{4}{8} + \dfrac{5}{10} = \dfrac{9}{9} \\ \\ \\ \sf \implies \dfrac{1}{2} + \dfrac{1}{2} = 1 \\ \\ \\ \sf \implies 1 = 1 \\ \\ \\ \tt LHS = RHS \\ \\ \\ \textbf{\underline{Hence verified}}$