Solve for x- 1-x-1-3-5 x-1-5-x-4- x-1-1-5-4

Given, 1/x + 1 + 3/5x+1=5/x+4 ⇒1/x+1 5/x+4 = 3/5x + 1 ⇒(x+4 ) 5 (x + 1 )/(x + 1 ) (x + 4 ) = 3/5x + 1 ⇒x+4 5x 5/x^2+5x + 4 = 3/5x+1 ( 4x 1 )/x^2 + 5x ...

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Byju's Answer

Standard X

Mathematics

Solving a Quadratic Equation by Factorization Method

Solve for x: ...

Question

Solve for x: $\frac{1}{x + 1} + \frac{3}{5 x + 1} = \frac{5}{x + 4}, x \neq - 1, - \frac{1}{5}, - 4$

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Solution

Given, $\frac{1}{x + 1} + \frac{3}{5 x + 1} = \frac{5}{x + 4} \Rightarrow \frac{1}{x + 1} - \frac{5}{x + 4} = \frac{- 3}{5 x + 1} \Rightarrow \frac{(x + 4) - 5 (x + 1)}{(x + 1) (x + 4)} = \frac{- 3}{5 x + 1} \Rightarrow \frac{x + 4 - 5 x - 5}{x^{2} + 5 x + 4} = \frac{- 3}{5 x + 1} \frac{(- 4 x - 1)}{x^{2} + 5 x + 4} = \frac{- 3}{5 x + 1} \Rightarrow (4 x + 1) (5 x + 1) = 3 (x^{2} + 5 x + 4) \Rightarrow 20 x^{2} + 4 x + 5 x + 1 = 3 x^{2} + 15 x + 12 \Rightarrow 17 x^{2} - 6 x - 11 = 0 \Rightarrow 17 x^{2} - 17 x + 11 x - 11 = 0 \Rightarrow 17 x (x - 1) + 11 (x - 1) = 0 \Rightarrow (x - 1) (17 x + 11) = 0 \Rightarrow E i t h e r x = 1 o r x = \frac{- 11}{17}$

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Similar questions

Solve each of the following quadratic equations:
(i) $\frac{1}{x + 1} + \frac{2}{x + 2} = \frac{5}{x + 4}, x \neq - 1, - 2, - 4$
(ii) $\frac{1}{x + 1} + \frac{3}{5 x + 1} = \frac{5}{x + 4}, x \neq - 1 \frac{1}{5}, - 4$

Q. Solve for

x

(5 x + 1) (x + 3) - 8

=

5 (x + 1) (x + 2)

Q. Solve for x :

s i n^{- 1} \frac{3 x}{5} + s i n^{- 1} \frac{4 x}{5} = s i n^{- 1} x

x = 0, 1, - 1

Q. Solve the equation

x^{5} - 5 x^{4} + 9 x^{3} - 9 x^{2} + 5 x - 1 = 0

Solve for

x

5^{1 + {log}_{4} x} + 5^{{log}_{\frac{1}{4}} x - 1} = \frac{26}{5}

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Solve for x: 1x+1+35x+1=5x+4,x≠−1,−15,−4

Solve for x: $\frac{1}{x + 1} + \frac{3}{5 x + 1} = \frac{5}{x + 4}, x \neq - 1, - \frac{1}{5}, - 4$