Can someone please show me the steps to do these 2 problems? I just need to see where I'm making my mistakes.
3/a + 1/2 = 11/5a
4/y+2 = 1 - 8/y(y+2)
3/a + 1/2 = 11/5a
4/y+2 = 1 - 8/y(y+2)
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1) Multiply both sides by a.
a(3/a + 1/2) = a(11/5a)
a * (3/a) + a * (1/2) = a * (11/5a)
3 + a/2 = 11/5
Multiply both sides by 2.
2(3 + a/2) = 2(11/5)
6 + a = 22/5
Multiply both sides by 5.
5(6 + a) = 5(22/5)
30 + 5a = 22
5a = -8
a = -8/5
2) Mulitply both sides by y+2.
(y+2)(4/(y+2)) = (y+2)(1 - 8/(y(y+2)))
4 = y+2 - 8/y
Multiply both sides by y.
y(4) = y(y + 2 - 8/y)
4y = y^2 + 2y - 8
y^2 - 2y - 8 = 0
(y - 4)(y + 2) = 0
y - 4 = 0 or y + 2 = 0
y = 4 or y = -2
y = -2 forces us to divide by zero so we get rid of this.
y = 4
a(3/a + 1/2) = a(11/5a)
a * (3/a) + a * (1/2) = a * (11/5a)
3 + a/2 = 11/5
Multiply both sides by 2.
2(3 + a/2) = 2(11/5)
6 + a = 22/5
Multiply both sides by 5.
5(6 + a) = 5(22/5)
30 + 5a = 22
5a = -8
a = -8/5
2) Mulitply both sides by y+2.
(y+2)(4/(y+2)) = (y+2)(1 - 8/(y(y+2)))
4 = y+2 - 8/y
Multiply both sides by y.
y(4) = y(y + 2 - 8/y)
4y = y^2 + 2y - 8
y^2 - 2y - 8 = 0
(y - 4)(y + 2) = 0
y - 4 = 0 or y + 2 = 0
y = 4 or y = -2
y = -2 forces us to divide by zero so we get rid of this.
y = 4
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3/a + 1/2 =
lcd = 2*a
(6 + a)/(2*a)
4/y + 2 =
lcd = y
(4 + 2*y)/y = 2*(2 + y)/y
lcd = 2*a
(6 + a)/(2*a)
4/y + 2 =
lcd = y
(4 + 2*y)/y = 2*(2 + y)/y