Question

Решите 5/b-5 +1/b = a^2/b(a-3) - 9/b(a-3) = 6x/x^2-y^2 + 3/x+y =

Answer 1

1) (5×b+1×(b-5))/b(b-5)=(5b+b-5)/b(b-5)=(6b-5)/b(b-5)

2) (a²-9)/b(a-3)=(a-3)×(a+3)/b(a-3)=(a+3)/b

3) 6x+3×(x-y)/x²-y²=(6x+3x-3y)/x²-y²=(9x-3y)/x²-y²).

Answer 2

To solve the given equations, we'll start with the first one:

1. 5/b - 5 + 1/b = a^2/b(a-3) - 9/b(a-3)

To solve this equation, we need to find the value of 'a' in terms of 'b.' Let's proceed step by step:

Step 1: Get a common denominator for the fractions on both sides of the equation. The common denominator for the left side is 'b,' and for the right side is 'b(a-3).' So, we'll rewrite the equation as follows:

(5(a-3) - 5b + 1)/b = (a^2 - 9)/b(a-3)

Step 2: Eliminate the denominators by multiplying both sides by 'b(a-3).'

b(a-3)(5(a-3) - 5b + 1) = b(a-3)(a^2 - 9)

Step 3: Expand and simplify.

b(a^2 - 3a - 5a + 15 - 5b + 1) = b(a^3 - 9a - 3a^2 + 27)

Step 4: Further simplify and gather like terms.

b(a^2 - 8a + 16 - 5b) = b(a^3 - 3a^2 - 9a + 27)

Step 5: Now, since both sides are equal, the coefficients of 'b' on both sides must be equal, and the coefficients of 'a' on both sides must be equal.

a^2 - 8a + 16 - 5b = a^3 - 3a^2 - 9a + 27

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

a^3 - 3a^2 - 9a + 27 - a^2 + 8a - 16 + 5b = 0

Step 7: Combine like terms.

a^3 - 4a^2 - a + 11 + 5b = 0

This is the equation in terms of 'a' and 'b.' However, since there is no additional information given, we cannot solve for specific values of 'a' and 'b' without more context or additional equations.

Now, let's move on to the second equation:

2. 6x/(x^2-y^2) + 3/(x+y) = 0

To solve this equation, we need to simplify the left-hand side and set it to zero:

Step 1: Factor the denominator x^2 - y^2.

(x^2 - y^2) = (x + y)(x - y)

Step 2: Rewrite the equation with the factored denominator.

6x/[(x + y)(x - y)] + 3/(x + y) = 0

Step 3: Get a common denominator for the fractions on the left side.

The common denominator is (x + y)(x - y). So, we'll rewrite the equation as follows:

[6x + 3(x - y)] / [(x + y)(x - y)] = 0

Step 4: Combine like terms in the numerator.

[6x + 3x - 3y] / [(x + y)(x - y)] = 0

Step 5: Combine terms in the numerator.

(9x - 3y) / [(x + y)(x - y)] = 0

Step 6: Set the numerator to zero (since the fraction is zero when the numerator is zero).

9x - 3y = 0

Step 7: Solve for 'y.'

3y = 9x

y = 3x

So, the solution to the second equation is 'y = 3x.'

If there are more equations or specific values given for 'a,' 'b,' 'x,' and 'y,' we can further solve for them. Otherwise, the above results are the solutions to the given equations.