Solve if possible?

Question

1. 4/T=5/T-1/2

2. 4/T-3+2T/T-3=12/T^2-6T+9

Answer 1

1. 4/T=5/T-1/2

Multiply both sides by the LCD ie 2T

8 = 10 - T

So T = 2

CheckingSolutions:

4/2 = 5/2 - 1/2
2 = 2 1/2 - 1/2 TRUE!!!!

2. 4/(T-3)+2T/(T-3)=12/(T^2-6T+9)
(Assuming this is what you ACTUALLY meant!!!

So 4/(T-3)+2T/(T-3)=12/(T- 3)^2
Multiply both sides by LCD ie (T - 3)^2

Thus 4(T - 3) + 2T(T - 3) = 12

ie 2(T - 3) + T(T - 3) = 6

So 2T - 6 + T^2 - 3T - 6 = 0

ie T^2 - T - 12 = 0

So (T - 4)(T + 3) = 0

ie T = -3, 4

CHECKING Solutions:

4/T-3+2T/T-3=12/(T^2-6T + 9)

When T = -3
LHS = 4/-6 + -6/-6
= -2/-6
= 1/3
RHS = 12/(9 + 18 + 9)
= 12/36 = 1/3 = LHS TRUE!!!!!!!!!!!!!!!!

When T = 4
LHS = 4/1 + 8/1 = 12

RHS = 12/(16 - 24 + 9)
= 12 = LHS TRUE!!!!!!!!!!!!!!!!

Answer 2

1)
4/T = 5/T - 1/2

Multiply the equation by 2T (The LCM or GCF of the denominator) to eliminate the denominator (or the fractions)

2T(4/T = 5/T - 1/2)
8 = 10 -T
8 - 10 = 10 + 10 - T
-2 = - T
Divide by -1
-2/-1 = -T/-1
2 = T
T = 2 ===> the answer
To check
4/2 = 5/2 - 1/2
4/2 = 4/2
2 = 2

2)

Answer 3

1.4/T = 5 /T - 1/2
The above equation can be written as
4/T - 5/T = -1/2
Multiplying through out by T we have,
4 - 5 = -T/2
-1 = -T/2 or 1 = T/2 or T = 2
T = 2.

2. 4/T-3+2T/T-3 = 12 /T^2-6T+9

Solving T^2-6T+9, T^2-3T-3T+9 = T(T-3)-3(T-3)=(T-3)^2
Hence 4/T-3+2T/T-3 = 12/(T-3)^2
Multiplying through out by (T-3)^2 we have,
4(T-3) + 2T(T-3) = 12
4T-12+2T^2-6T = 12
This can be written a 2T^2-2T-24 = 0
Dividing through out by 2,
T^2-T-12 = 0
T^2-4T+3T-12 = 0
T(T-4)+3(T-4) = 0
(T-4)(T+3) = 0
Hence T = 4 or -3

Answer 4

Question 1
4 / T = 5 / (T - 1/2)
4T - 2 = 5T
T = - 2

Question 2
4 / (T - 3) + 2T / (T - 3) = 12 / (T - 3)²
4.(T - 3) + 2T(T - 3) = 12
(T - 3).(4 + 2T) = 12
2T² - 2T - 24 = 0
(T² - T - 12) = 0
(T - 4).(T + 3) = 0
T = 4 , T = - 3

Answer 5

T=2;
just solve equation (1)
bring 4/T to the right hand side(RHS) and -1/2 to Left hand side(LHS),
it will be 1/2=5/T-4/T
1/2=1/T(5-4)
1/2=1/T(1)
1/2=1/T
cross multiply to get T=2