1.Solve (x)/(x+10)+(x-3)/(x+2)=7/5..I got that there is no solution, is that correct?
2. Solve (x)/(x-5)+1=(5)/(x-5)..I got that there is no solution for this one too, is that correct?
3. Express your result in simplest form, (4)/(xy)+(6)/(xy)..I got (10)/(xy) is that correct?
4. Simplify (3)/(4) divided by (4)/(5)...I got 15/16, is that right?
3 is correct.
2 has is indeterminate, in your language, that is probably no solution.
1 recheck.
1. To solve the equation (x)/(x+10) + (x-3)/(x+2) = 7/5, you need to combine the fractions on the left side by finding a common denominator.
The common denominator for the fractions (x)/(x+10) and (x-3)/(x+2) is (x+10)(x+2), as it contains both denominators.
Multiplying each fraction by the appropriate denominator, we get:
[(x)(x+2)]/[(x+10)(x+2)] + [(x-3)(x+10)]/[(x+10)(x+2)] = 7/5
Expanding and combining like terms, we have:
[(x^2 + 2x) + (x^2 + 7x - 30)]/[(x+10)(x+2)] = 7/5
Simplifying further, we have:
[2x^2 + 9x - 30]/[(x+10)(x+2)] = 7/5
To solve for x, we can cross-multiply:
5(2x^2 + 9x - 30) = 7[(x+10)(x+2)]
Expanding and simplifying this equation leads to a quadratic equation:
10x^2 + 45x - 150 = 7(x^2 + 12x + 20)
10x^2 + 45x - 150 = 7x^2 + 84x + 140
Rearranging the terms:
3x^2 + 39x - 290 = 0
Using the quadratic formula or factoring, we find that this equation has no real solutions. Therefore, your initial observation that there is no solution is correct.
2. To solve the equation (x)/(x-5) + 1 = 5/(x-5), start by subtracting 1 from both sides:
(x)/(x-5) = 4/(x-5)
Now, cross-multiply to remove the denominators:
x(x-5) = 4(x-5)
Expanding the equation:
x^2 - 5x = 4x - 20
Rearranging the terms:
x^2 - 9x + 20 = 0
Factoring this equation gives:
(x-4)(x-5) = 0
This equation has two solutions: x = 4 and x = 5. Therefore, your initial observation that there is no solution is incorrect. The correct answer is that x = 4 and x = 5 are both solutions to the equation.
3. The expression (4)/(xy) + (6)/(xy) can be simplified by combining the like terms. Since the denominators are the same, we can add the numerators:
(4+6)/(xy) = 10/(xy)
Therefore, your simplified result of (10)/(xy) is correct.
4. To simplify (3)/(4) divided by (4)/(5), we can multiply by the reciprocal of the divisor:
(3)/(4) ÷ (4)/(5) = (3)/(4) x (5)/(4)
Now, multiply the numerators and the denominators:
(3x5)/(4x4) = 15/16
So, your simplified result of 15/16 is correct.