1963 TMTA High School Algebra I Contest Problem 35

Problem

Combine and simplify $\frac{2}{6-3x}+\frac{5}{x-2}-\frac{3}{4-2x}$

$\text{(A)} \quad \frac{-35}{6(x-2)} \quad \text{(B)} \quad \frac{-35}{6(2-x)} \quad \text{(C)} \quad \frac{35}{6(2-x)}$

$\text{(D)} \quad \frac{6}{2-x} \quad \text{(E)} \quad \frac{6}{x-2}$

The common denominator is $(2)(3)(x-2).$ $\frac{2}{6-3x}+\frac{5}{x-2}-\frac{3}{4-2x}=\frac{(-2)+6(5)-(-3)}{(2)(3)(x-2)}=\frac{35}{6x-12}$

The answer is $\boxed{\text{(B)}}.$

1963 TMTA High School Mathematics Contests (Problems)
Preceded by Problem 34	TMTA High School Mathematics Contest Past Problems/Solutions	Followed by Problem 36