Question

Help solve for number 6 please !!
:)

Answer 1

x: {-3, 5}

Explanation:

Step 1. Find least common denominator

Step 2. Multiply missing factors on top AND bottom

Step 3. Combine like terms

Step 4. Simplify (get rid of denominator)

Step 5. Solve for x

`(x)/(x-5) +(3)/(x+2) =(7x)/(x^2-3x-10)` LCD =
`x^2-3x-10` OR
`(x-5)(x+2)`

`(x)/(x-5)((x+2)/(x+2)) +(3)/(x+2)((x-5)/(x-5)) =(7x)/(x^2-3x-10)`

`(x(x+2))/((x-5)(x+2)) +(3(x-5))/((x+2)(x-5)) =(7x)/((x-5)(x+2))`

`(x(x+2)+3(x-5))/((x-5)(x+2)) =(7x)/((x-5)(x+2))`

`(x^2+2x+3x-15)/((x-5)(x+2)) =(7x)/((x-5)(x+2))`

`(x^2+5x-15)/((x-5)(x+2)) =(7x)/((x-5)(x+2))`

`x^2+5x-15=7x`

`x^2-2x-15`

`(x-5)(x+3)`

x = -3, 5