Question

3) (3x ^ 2 - 1)/(x + 1) = 3x 4) (9x - 7)/(3x - 2) - (4x - 5)/(2x - 3) = 1 5) (x ^ 2 - 9)/(x ^ 2 + 3x) = (x - 3)/x + (x + 2)/(x + 3)

Answer 1

Відповідь:

3) x=-0.3

4) x=1

5) x=2

Пояснення:

Answer 2

Let's solve each equation step by step:

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

To begin, we can multiply both sides of the equation by (x + 1) to eliminate the denominator:

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

Expanding the right side:

3x^2 - 1 = 3x^2 + 3x

Now, let's simplify by moving all terms to one side of the equation:

3x^2 - 3x^2 - 3x - 1 = 0

Simplifying further:

-3x - 1 = 0

To isolate x, we can add 1 to both sides:

-3x = 1

And then divide both sides by -3:

x = -1/3

Therefore, the solution to the equation is x = -1/3.

4. (9x - 7)/(3x - 2) - (4x - 5)/(2x - 3) = 1

To start, let's find a common denominator for the fractions on the left side of the equation. The common denominator is (3x - 2)(2x - 3):

[(9x - 7)(2x - 3)]/[(3x - 2)(2x - 3)] - [(4x - 5)(3x - 2)]/[(2x - 3)(3x - 2)] = 1

Expanding the numerators:

[18x^2 - 27x - 14x + 21]/[(3x - 2)(2x - 3)] - [12x^2 - 8x - 15x + 10]/[(2x - 3)(3x - 2)] = 1

Simplifying the numerators:

(18x^2 - 41x + 21)/[(3x - 2)(2x - 3)] - (12x^2 - 23x + 10)/[(2x - 3)(3x - 2)] = 1

Now, let's find a common denominator for the fractions on the left side:

[(18x^2 - 41x + 21) - (12x^2 - 23x + 10)]/[(3x - 2)(2x - 3)] = 1

Expanding and combining like terms:

(18x^2 - 41x + 21 - 12x^2 + 23x - 10)/[(3x - 2)(2x - 3)] = 1

(6x^2 - 18x + 11)/[(3x - 2)(2x - 3)] = 1

Multiplying both sides by [(3x - 2)(2x - 3)] to eliminate the denominator:

6x^2 - 18x + 11 = (3x - 2)(2x - 3)

Expanding the right side:

6x^2 - 18x + 11 = 6x^2 - 11x - 6x + 6

Simplifying:

6x^2 - 18x + 11 = 6x^2 - 17x + 6

Moving all terms to one side of the equation:

6x^2 - 6x^2 - 18x + 17x + 11 - 6 = 0

Simplifying further:

-x + 5 = 0

To isolate x