Question

(4x-3/x+1)-(2/1-x^2)=x/x-1

Answer 1

1) разложить 1-x^2=(1-x)(1+x)
(4x-3/x+1)-(2/(1-x)(1+x))=
общий знаменатель будет (1-x)(1+x)
=((4x-3)(1-x)-2)/(1-x)(1+x)=
=(4x-4x^2-3+3x-2)/(1-x)(1+x) (-4x^2+7x+5)/(1-x)(1+x)=(x/x-1)
(-4x^2+7x+5)/(1-x)(1+x)*-(1-x/x)=0
(-4x^2+7x+5)/(1+x)*-x)

Answer 2

To solve the equation $\frac{4x-3}{x+1} - \frac{2}{1-x^2} = \frac{x}{x-1}$, we can start by finding a common denominator and then combining the fractions on the left-hand side.

The common denominator for the first and second fractions is $(x+1)(1+x)$, which simplifies to $-(x^2 - 1)$ using the difference of squares. So, let's rewrite the equation with a common denominator:

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

Now, you can simplify the equation:

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

Expand the expressions:

$4x - 4x^3 - 3 + 3x^2 - 2x - 2 = x(1-x^2)$

Now, simplify further:

$-4x^3 + 3x^2 + 2x - 5 = x - x^3$

Now, let's move all terms to one side of the equation:

$-4x^3 + x^3 + 3x^2 - x + 2x - 5 - x = 0$

Combine like terms:

$-3x^3 + 3x^2 - 6x - 5 = 0$

Now, you have a cubic equation. To solve this cubic equation, you can use numerical methods, such as graphing, factoring, or the Rational Root Theorem to find rational roots if they exist.

Without numerical methods, finding an exact solution for this equation can be quite complex, and you may need to use a computer or calculator to approximate the solutions.