Question

solve the following equation :​

Answer 1

Answer:

$\frac{1}{x - 1} - \frac{1}{x} = \frac{1}{x + 3} - \frac{1}{x + 4} \\ \frac{x - (x - 1)}{(x - 1)x} = \frac{(x + 4) - (x + 3)}{(x + 3)(x + 4)} \\ \frac{x - x + 1}{ {x}^{2} - x } = \frac{x + 4 - x - 3}{ {x}^{2} + 3x + 4x + 12} \\ \frac{1}{ {x}^{2} - x} = \frac{1}{ {x}^{2} + 7x + 12} \\ {x}^{2} + 7x + 12 = {x}^{2} - x \\ 7x + x = - 12 \\ 8x = - 12 \\ x = - \frac{ 12}{8} \\ x = - \frac{3}{2}$

This is solution of your question.

Answer 2

Answer:

-1.5

Step-by-step explanation:

Variable x cannot be equal to any of the values −4,−3,0,1 since division by zero is not defined. Multiply both sides of the equation by x(x−1)(x+3)(x+4), the least common multiple of x−1,x,x+3,x+4.

             x(x+3)(x+4)−(x−1)(x+3)(x+4)=x(x−1)(x+4)−x(x−1)(x+3)

Use the distributive property to multiply x by x+3.

              (x^2  +3x)(x+4)−(x−1)(x+3)(x+4)=x(x−1)(x+4)−x(x−1)(x+3)

Use the distributive property to multiply x ^2 +3x by x+4 and combine like terms.

               x ^3 +7x ^2 +12x−(x−1)(x+3)(x+4)=x(x−1)(x+4)−x(x−1)(x+3)

Use the distributive property to multiply x  ^2 +3x by x+4 and combine like terms.

x  ^3 +7x  ^2 +12x−(x−1)(x+3)(x+4)=x(x−1)(x+4)−x(x−1)(x+3)

Then solve like this type

x=−  3/2

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