Question

Show that 2/4-x= 10/4+x is equivalent to 12x=22 for all values of x not equal to 4 or -4

Answer 1

Step 1:

Write out the expression

`(2)/(4-x)=(10)/(4+x),x\\e4,x\\e-4`

Step 2:

We cross-multiply, to get

`2(4+x)=10(4-x)`

Step 3:

we expand the expression

`8+2x=40-10x`

Step 4

We collect like terms

`\begin{gathered} 2x+10x=40-8 \\ \text{ Hence, we have} \\ 12x=32 \end{gathered}`