Question

x-3/x-4 + x-5/x-6 =10/3.

Answer 1

Answer:

Step-by-step explanation:

Answer 2

x-3/x-4 + x-5/x-6=10/3

By Taking LCM:

(x-3)(x-6)+(x-5)(x-4)/(x-4)(x-6) =10/3

(x2+6x-3%x+18)+(x2-4x-6x+20) =10

x2-6x-4x+24 3

2x2-18x+38 = 10

x2-10x+24 3

Cross Multiplication:

(2x2-18x+38)3=(x2-10x+24)10

6x2-54x+114=10x-100x+240

Bringing left side terms to right side:

0=10x2-6x2-100x+54x+240-114

0=4x2-46x+126

4x2-46x+126=0

To Make It Simpler:

2÷) 4x2-46x+126=0

2x2-23x+63=0

you can use any formula and here im using the following formula:

-b+-root b2 -4ac

2a

-23+- root ((-23)^2 - 4(2)(63))

2(2)

-23+- root(529-4(126))

4

-23+- root (529-504)

4

-23+-root(25)

4

Root and square gets cancelled:

-23+- 5

4

-23+5 -23-5

4 4

-18 -28

4 4

-9 -7

2 1

x- 9/2 =0 x-7=0

x=9/2 x=7