Question

(x+6)/(x+5)-(2x-1/(x-4)+(x+4)/(x-2)=0. solve​

Answer 1

Answer:

There's only one thing to do....

Take lcm and expand.

Note that as x can be negative, the denominator won't be cancelled.

Solve by wavy curve method and get the range of the values of X.

Hope this helps....

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Answer 2

Your Question :

$\sf{{Solve \: \frac{x + 6}{x + 5} - \frac{2x - 1}{x - 4} + \frac{x + 4}{x - 2} }{ \: = \: 0 }}$

Given :

• $\sf{{Algebraic \: expression → \: \frac{x + 6}{x + 5} - \frac{2x - 1}{x - 4} + \frac{x + 4}{x - 2} }{ \: = \: 0 }}$

To Do :

• Solve the given equation
• Find the value of x

Solution :

Multiplying both the sides by the LCM of the denominators , i.e. by (x + 5)(x - 4)(x - 2),

➯ (x + 6)(x - 4)(x - 2) - (2x - 1)(x + 5)(x - 2) + (x + 4)(x + 5)(x - 4) = 0

: ⟼ (x + 6){x² - (4 + 2)x + 4 × 2} - (2x - 1){x² + (5 - 2)x - 5 × 2} + (x + 5)(x² - 16) = 0

: ⟼ (x + 6)(x² - 6x + 8) - (2x - 1)(x² + 3x - 10) + (x + 5)(x² - 16) = 0

: ⟼ x(x² - 6x + 8) + 6(x² - 6x + 8) - 2x(x² + 3x - 10) + x² + 3x - 10 + x(x² - 16) = 0

: ⟼ x³ - 6x² + 8x + 6x² - 36x + 48 - 2x³ - 6x² + 20x + x² + 3x - 10 + x³ - 16x + 5x² - 80 = 0

: ⟼ 8x - 36x + 48 + 20x + 3x - 10 - 16x - 80 = 0

: ⟼ -21x - 42 = 0

: ⟼ 21x = -42

$\sf{{ : \: ⟼ \: x = \frac{ - 42}{21} = -2\: }{ \: }}$

Therefore :

∴ The value of x is -2.

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