Question

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

Answer 1

Ответ:

(х+3)(х-1)=(2х+3)(2х-2)

х²+3х-х-3=4х²+6х-4х-6

х²+2х-3-4х²-2х+6=0

-3х²+3=0

-3х²=-3

х²=1

х1=-1 х2=1

Answer 2

Ответ:

нет решений

Пошаговое объяснение:

$\frac{x+3}{x-1} = \frac{2x+3}{2x-2}$. ОДЗ: $x\neq 1$

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

$2(x+3)=2x+3$

$2x+6=2x+3$

$6=3$, противоречие, значит уравнение не имеет решений.

Answer 3

To solve the equation $\frac{{x+3}}{{x - 1}} = \frac{{2x+3}}{{2x - 2}}$, you can follow these steps:

Step 1: Find a common denominator. The common denominator for both fractions is $(x - 1)(2x - 2)$.

Step 2: Rewrite the fractions with the common denominator. $\frac{{x+3}}{{x - 1}} = \frac{{2x+3}}{{2x - 2}}$ can be rewritten as:

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

Step 3: Cross-multiply. Cross-multiply to eliminate the denominators:

$(x+3)(2x - 2) = (2x+3)(x - 1)$.

Step 4: Expand and simplify. Expand both sides of the equation and simplify:

$2x^2 + 4x - 2x - 6 = 2x^2 - 2x + 3x - 3$.

Step 5: Combine like terms. Combine like terms on both sides of the equation:

$2x^2 + 2x - 6 = 2x^2 + x - 3$.

Step 6: Subtract $2x^2$ from both sides. Subtract $2x^2$ from both sides to eliminate the quadratic terms:

$2x - 6 = x - 3$.

Step 7: Isolate $x$. Subtract $x$ from both sides to isolate $x$:

$x - 6 = -3$.

Step 8: Add 6 to both sides. Add 6 to both sides to solve for $x$:

$x = -3 + 6$.

Step 9: Simplify the result. $x = 3$.

So, the solution to the equation is $x = 3$.