Question

Solve the equation. Check for extraneous solutions.
[(x-4)/(x-1)]=[(10)/(x-7)]
Please show work b/c i don't understand how to solve this correctly. Thank you.

Answer 1

multiply, combine like terms , and set the equation equal to 0

Answer 2

cross multiply?

Answer 3

yes

Answer 4

\[\frac{x-4}{x-1}=\frac{10}{x-7}\]Multiply both sides by (x-7) and then by (x-1)\[(x-7)(x-4) = 10(x-1)\]\[x^{2}-11x+28 = 10x-10\]\[x^{2}-21x+38 = 0\]Factor the quadratic:\[(x-19)(x-2)=0\]So x is 19 or 2

Answer 5

factor and .... too late the solution is up ...

Answer 6

check solutions to make sure they are not extraneous ...