4/ (z-1) - 5 / (z+2) =3 / z Pls solve this equation
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Answered by
22
Solution⇒
⇒ 4 - 5 = 3
------- --------- -----
z - 1 z + 2 z
⇒ 4z + 8 - (5z - 5) = 3
--------------------- ----
z² - z + 2z -2 z
⇒4z - 5z + 8 + 5 = 3
------------------ -----
z² + z - 2 z
⇒(-z + 13)z = 3z² + 3z - 6
⇒-z² + 13z = 3z² + 3z - 6
⇒3z² + 3z - 6 + z² - 13z = 0
⇒4² - 10z - 6 = 0
Dividing whole equation by 2
⇒2z² - 5z - 3=0
⇒2z² - 6z + z - 3=0
⇒2z(z - 3) + 1(z - 3) = 0
⇒(2z + 1) (z - 3) = 0
⇒2z + 1 = 0 OR z - 3=0
2z = -1 z = 3
z = -1/2
Therfore,
z = -1/2 OR z = 3
⇒ 4 - 5 = 3
------- --------- -----
z - 1 z + 2 z
⇒ 4z + 8 - (5z - 5) = 3
--------------------- ----
z² - z + 2z -2 z
⇒4z - 5z + 8 + 5 = 3
------------------ -----
z² + z - 2 z
⇒(-z + 13)z = 3z² + 3z - 6
⇒-z² + 13z = 3z² + 3z - 6
⇒3z² + 3z - 6 + z² - 13z = 0
⇒4² - 10z - 6 = 0
Dividing whole equation by 2
⇒2z² - 5z - 3=0
⇒2z² - 6z + z - 3=0
⇒2z(z - 3) + 1(z - 3) = 0
⇒(2z + 1) (z - 3) = 0
⇒2z + 1 = 0 OR z - 3=0
2z = -1 z = 3
z = -1/2
Therfore,
z = -1/2 OR z = 3
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12
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