SOLUTION: {{{ (4a-3)= (a+33)/(a+1) }}} Please help with this rational expression. I have gotten this far..4a-3 multiplied by a+1/a+33= 4a^2+3/a+33

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: {{{ (4a-3)= (a+33)/(a+1) }}} Please help with this rational expression. I have gotten this far..4a-3 multiplied by a+1/a+33= 4a^2+3/a+33      Log On


   

Question 307388: +%284a-3%29=+%28a%2B33%29%2F%28a%2B1%29+
Please help with this rational expression. I have gotten this far..4a-3 multiplied by a+1/a+33= 4a^2+3/a+33
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
+%284a-3%29=+%28a%2B33%29%2F%28a%2B1%29+ Start with the given equation.


+%284a-3%29%28a%2B1%29=+a%2B33+ Multiply both sides by a%2B1.


+4a%5E2%2Ba-3=+a%2B33+ FOIL


4a%5E2%2Ba-3-a-33=0 Get every term to the left side.


4a%5E2%2B0a-36=0 Combine like terms.


Notice that the quadratic 4a%5E2%2B0a-36 is in the form of Aa%5E2%2BBa%2BC where A=4, B=0, and C=-36


Let's use the quadratic formula to solve for "a":


a+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


a+=+%280+%2B-+sqrt%28+%280%29%5E2-4%284%29%28-36%29+%29%29%2F%282%284%29%29 Plug in A=4, B=0, and C=-36


a+=+%280+%2B-+sqrt%28+0-4%284%29%28-36%29+%29%29%2F%282%284%29%29 Square 0 to get 0.


a+=+%280+%2B-+sqrt%28+0--576+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-36%29 to get -576


a+=+%280+%2B-+sqrt%28+0%2B576+%29%29%2F%282%284%29%29 Rewrite sqrt%280--576%29 as sqrt%280%2B576%29


a+=+%280+%2B-+sqrt%28+576+%29%29%2F%282%284%29%29 Add 0 to 576 to get 576


a+=+%280+%2B-+sqrt%28+576+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


a+=+%280+%2B-+24%29%2F%288%29 Take the square root of 576 to get 24.


a+=+%280+%2B+24%29%2F%288%29 or a+=+%28-0+-+24%29%2F%288%29 Break up the expression.


a+=+%2824%29%2F%288%29 or a+=++%28-24%29%2F%288%29 Combine like terms.


a+=+3 or a+=+-3 Simplify.


So the solutions are a+=+3 or a+=+-3