Question

Help me please. Finals are next week and i’m stuck.

Answer 1

x = 0, x = 7

Explanation:

Given equation:

`\implies (x+3)/(x-3)+(x)/(x-5)=(x+5)/(x-5)`

Multiply by (x - 5):

`\implies ((x+3)(x-5))/(x-3)+(x(x-5))/(x-5)=((x+5)(x-5))/(x-5)`

Factor out common term (x - 5):

`\implies ((x+3)(x-5))/(x-3)+x=x+5`

Multiply by (x - 3):

`\implies ((x+3)(x-5)(x-3))/(x-3)+x(x-3)=(x+5)(x-3)`

Factor out common term (x - 3):

`\implies (x+3)(x-5)+x(x-3)=(x+5)(x-3)`

Expand brackets:

`\implies x^2-5x+3x-15+x^2-3x=x^2-3x+5x-15`

Combine like terms:

`\implies 2x^2-5x-15=x^2+2x-15`

Simplify:

`\implies x^2-7x=0`

Factor and solve:

`\implies x(x-7)=0`

`\implies x=0,7`