How do you solve 8x−4−3=1x−10?
1 Answer
Explanation:
The first thing to notice here is that you have two values of
This means that any possible solution set will not include thes values. In other words, you need
x−4≠0⇒x≠4 andx−10≠0⇒x≠10
The next thing to do is use the common denominator of the two fractions, which is equal to
To do that, multiply the first fraction by
This will get you
8x−4⋅x−10x−10−3⋅(x−4)(x−10)(x−4)(x−10)=1x−10⋅x−4x−4
8(x−10)(x−4)(x−10)−3(x−4)(x−10)(x−4)(x−10)=x−4(x−4)(x−10)
This is of course equivalent to
8x−80−3(x2−14x+40)=x−4
7x−76−3x2+42x−120=0
3x2−49x+196=0
Use the quadratic formula to find the two roots of this quadratic equation
x1,2=−(−49)±√(−49)2−4⋅3⋅1962⋅3
x1,2=49±√496=49±76
Therefore, you have
x1=49−76=7 andx2=49+76=283
Since both solutions satisfy the condtions
