Answer:
To simplify the equation (2p/p^2 - 25) - (3/p - 5) = 5/(p + 5), you can follow these steps:
1. Factor the denominator in the first fraction and the second fraction:
(2p/[(p + 5)(p - 5)]) - (3/(p - 5)) = 5/(p + 5)
2. Find a common denominator for all three fractions, which is (p + 5)(p - 5):
(2p - 3(p + 5))/[(p + 5)(p - 5)] = 5/(p + 5)
3. Distribute the -3 on the left side of the equation:
(2p - 3p - 15)/[(p + 5)(p - 5)] = 5/(p + 5)
4. Combine like terms in the numerator:
(-p - 15)/[(p + 5)(p - 5)] = 5/(p + 5)
5. Cross-multiply to get rid of the fractions:
(-p - 15)(p + 5) = 5[(p + 5)(p - 5)]
6. Expand both sides:
-p^2 - 15p + 5p + 75 = 5(p^2 - 25)
7. Simplify further:
-p^2 - 10p + 75 = 5p^2 - 125
8. Move all terms to one side of the equation:
-p^2 - 10p + 75 - 5p^2 + 125 = 0
9. Combine like terms:
-6p^2 - 10p + 200 = 0
10. Divide the equation by -2 to simplify further:
3p^2 + 5p - 100 = 0
Now you have a quadratic equation. You can solve it using the quadratic formula or factoring to find the values of 'p' that satisfy this equation.
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Verified answer
Answer:
To simplify the equation (2p/p^2 - 25) - (3/p - 5) = 5/(p + 5), you can follow these steps:
1. Factor the denominator in the first fraction and the second fraction:
(2p/[(p + 5)(p - 5)]) - (3/(p - 5)) = 5/(p + 5)
2. Find a common denominator for all three fractions, which is (p + 5)(p - 5):
(2p - 3(p + 5))/[(p + 5)(p - 5)] = 5/(p + 5)
3. Distribute the -3 on the left side of the equation:
(2p - 3p - 15)/[(p + 5)(p - 5)] = 5/(p + 5)
4. Combine like terms in the numerator:
(-p - 15)/[(p + 5)(p - 5)] = 5/(p + 5)
5. Cross-multiply to get rid of the fractions:
(-p - 15)(p + 5) = 5[(p + 5)(p - 5)]
6. Expand both sides:
-p^2 - 15p + 5p + 75 = 5(p^2 - 25)
7. Simplify further:
-p^2 - 10p + 75 = 5p^2 - 125
8. Move all terms to one side of the equation:
-p^2 - 10p + 75 - 5p^2 + 125 = 0
9. Combine like terms:
-6p^2 - 10p + 200 = 0
10. Divide the equation by -2 to simplify further:
3p^2 + 5p - 100 = 0
Now you have a quadratic equation. You can solve it using the quadratic formula or factoring to find the values of 'p' that satisfy this equation.