Question

X+3/x+2=x-1/x-7................

Answer 1

$\frac{x+3}{x+2} = \frac{x-1}{x-7} \\ \\ (x+3)(x-7)=(x+2)(x-1) \\ \\ x^2-7x+3x-21=x^2-x+2x-2 \\ \\ x^2-7x+3x-x^2+x-2x=-2+21 \\ \\ -5x=19 |:(-5) \\ \\ x=-3.8$

Answer 2

To solve the equation $\frac{x+3}{x+2} = \frac{x-1}{x-7}$, you can start by cross-multiplying to get rid of the fractions. Here are the steps to solve the equation:

1. Cross-multiply: $(x+3)(x-7) = (x-1)(x+2)$

2. Expand both sides of the equation: $x^2 - 7x + 3x - 21 = x^2 + 2x - x - 2$

3. Simplify and group like terms: $x^2 - 4x - 21 = x^2 - x - 2$

4. Subtract $x^2$ from both sides to cancel out the $x^2$ terms: $-4x - 21 = -x - 2$

5. Add $4x$ to both sides to isolate the $x$ terms on the left side: $-21 = 3x - 2$

6. Add 2 to both sides to further isolate the $3x$ term: $-19 = 3x$

7. Finally, divide both sides by 3 to solve for $x$: $x = -19/3$

So, the solution to the equation is $x = -19/3$.

Answer 3

To solve the equation $\frac{x + 3}{x + 2} = \frac{x - 1}{x - 7}$, you can follow these steps:

1. Start by finding a common denominator for the fractions on both sides of the equation. In this case, the common denominator is $(x + 2)(x - 7)$. Rewrite the equation with this common denominator:

$\frac{x + 3}{x + 2} \cdot \frac{(x - 7)}{(x - 7)} = \frac{x - 1}{x - 7} \cdot \frac{(x + 2)}{(x + 2)}$.

This gives you:

$\frac{(x + 3)(x - 7)}{(x + 2)(x - 7)} = \frac{(x - 1)(x + 2)}{(x - 7)(x + 2)}$.

2. Now, since both sides of the equation have the same denominator, you can set the numerators equal to each other:

$(x + 3)(x - 7) = (x - 1)(x + 2)$.

3. Expand and simplify the equation:

$x^2 - 4x - 21 = x^2 + x - 2$.

4. Next, move all terms to one side of the equation to set it equal to zero:

$x^2 - x^2 - 4x - x - 21 + 2 = 0$.

This simplifies to:

$-5x - 19 = 0$.

5. Now, isolate the variable by adding 19 to both sides of the equation:

$-5x = 19$.

6. Finally, divide both sides by -5 to find the value of x:

$x = \frac{19}{-5}$.

Simplify this fraction:

$x = -\frac{19}{5}$.

So, the solution to the equation is $x = -\frac{19}{5}$.