How do you solve rational equations #[(x+2) / (x-1)] = [1/2]#?

Question

Hazel Anglin · Accepted Answer

#x=-5#

When we have a fraction equal to another fraction we can use the method of #color(blue)"cross-multiplication"# to solve.

That is #(color(red)(x+2))/(color(blue)(x-1))=color(blue)(1)/color(red)(2)#

Now multiply the terms on either end of an 'imaginary' cross (X). That is multiply the #color(red)("red")# values together and the #color(blue)("blue")# values together and equate them.

#rArrcolor(red)(2(x+2))=color(blue)(1(x-1))#

distribute the brackets.

#rArr2x+4=x-1#

We now want to have the x terms on the left of the equation and numeric values on the right.

subtract x from both sides.

#2x-x+4=cancel(x)cancel(-x)-1#

#rArrx+4=-1#

subtract 4 from both sides.

#xcancel(+4)cancel(-4)=-1-4#

#rArrx=-5" is the solution"#

Isaiah Anthony · Answer

undefined To solve the rational equation [(x+2) / (x-1)] = [1/2], you can start by cross-multiplying to eliminate the fractions. This gives you (x+2) * 2 = (x-1) * 1. Simplifying this equation, you get 2x + 4 = x - 1. Next, you can combine like terms by subtracting x from both sides, resulting in x + 4 = -1. Finally, you can isolate x by subtracting 4 from both sides, giving you x = -5. Therefore, the solution to the rational equation is x = -5.