Question

A) 3х+4 х^2 ---------- = ------------ х^2-16 = х^2-16

Answer 1

Ответ: –1

Объяснение: во вложении

Answer 2

To solve the equation (3x + 4) / (x^2 - 16) = (x^2 - 16) / (x^2 - 16), we need to first simplify both sides of the equation and then find the values of x that satisfy the equation.

Step 1: Simplify the equation

On the left-hand side of the equation, we notice that (x^2 - 16) / (x^2 - 16) is equal to 1, as any number divided by itself is always 1.

So the equation simplifies to:

(3x + 4) / (x^2 - 16) = 1

Step 2: Factor the denominator on the left-hand side

The denominator (x^2 - 16) is a difference of squares, so we can factor it:

x^2 - 16 = (x + 4)(x - 4)

Step 3: Rewrite the equation

Now, the equation becomes:

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

Step 4: Clear the fraction

To get rid of the fraction, we can multiply both sides of the equation by (x + 4)(x - 4):

(3x + 4) = (x + 4)(x - 4)

Step 5: Expand and simplify

Expand the right-hand side:

3x + 4 = x^2 - 4x + 4x - 16

The 4x and -4x cancel out, and we are left with:

3x + 4 = x^2 - 16

Step 6: Move all terms to one side to set the equation to zero

x^2 - 3x - 20 = 0

Step 7: Factor the quadratic equation

Now we can factor the quadratic equation:

(x - 5)(x + 4) = 0

Step 8: Solve for x

Setting each factor to zero and solving for x:

x - 5 = 0 --> x = 5

x + 4 = 0 --> x = -4

So, the solutions to the original equation are x = 5 and x = -4. These values satisfy the equation (3x + 4) / (x^2 - 16) = (x^2 - 16) / (x^2 - 16).