Question

5/(x – 1) – 3/(x + 1) = 15/(x2 – 1)

Answer 1

Ответ:

/ это умножения?

Объяснение:

сделано с любовью ️

Answer 2

To solve the equation 5/(x - 1) - 3/(x + 1) = 15/(x^2 - 1), you can follow these steps:

Step 1: Factor the denominator of the last term, which is x^2 - 1.

x^2 - 1 can be factored as (x - 1)(x + 1).

So, the equation becomes:

5/(x - 1) - 3/(x + 1) = 15/((x - 1)(x + 1))

Step 2: Find a common denominator for all the fractions on the left side of the equation. In this case, the common denominator is (x - 1)(x + 1).

Rewrite each fraction with this common denominator:

(5(x + 1))/((x - 1)(x + 1)) - (3(x - 1))/((x - 1)(x + 1)) = 15/((x - 1)(x + 1))

Step 3: Combine the fractions on the left side of the equation:

[5(x + 1) - 3(x - 1)]/((x - 1)(x + 1)) = 15/((x - 1)(x + 1))

Step 4: Simplify the numerators on the left side:

[5x + 5 - 3x + 3]/((x - 1)(x + 1)) = 15/((x - 1)(x + 1))

Now, combine like terms in the numerator:

(2x + 8)/((x - 1)(x + 1)) = 15/((x - 1)(x + 1))

Step 5: Cross-multiply to eliminate the denominators:

(2x + 8) * ((x - 1)(x + 1)) = 15 * ((x - 1)(x + 1))

Step 6: Expand both sides of the equation:

2x(x^2 - 1) + 8(x^2 - 1) = 15(x^2 - 1)

Step 7: Distribute and simplify further:

2x^3 - 2x + 8x^2 - 8 = 15x^2 - 15

Step 8: Rearrange the equation to set it equal to zero:

2x^3 + 8x^2 - 15x^2 - 2x - 8 + 15 = 0

Step 9: Combine like terms:

2x^3 - 7x^2 - 2x + 7 = 0

Step 10: Factor the equation, if possible. In this case, it may not factor easily, so you may need to use numerical methods or a calculator to find approximate solutions.

Unfortunately, this equation does not have simple rational solutions, so you would typically use numerical methods like graphing, a calculator, or a computer algebra system to approximate the solutions.