1. The problem asks first to find the values of $a$ and $b$ given the function $g(x) = ax + b$ and the graph is a straight line positioned at the center of the image. Since no specific points or details besides the centering are given, and considering the next part gives $g(x) = 4x + 1$, we directly take from the problem: $$a = 4,\quad b = 1$$ 2. Next, simplify the expression: $$\frac{2}{f(x)} - \frac{5}{g(x)}$$ where $$f(x) = 3x - 4$$ $$g(x) = 4x + 1$$ 3. Find a common denominator for the fractions, which is: $$(3x - 4)(4x + 1)$$ 4. Rewrite each fraction with the common denominator: $$\frac{2}{3x - 4} = \frac{2(4x + 1)}{(3x - 4)(4x + 1)}$$ $$\frac{5}{4x + 1} = \frac{5(3x - 4)}{(3x - 4)(4x + 1)}$$ 5. Subtract the fractions: $$\frac{2(4x + 1) - 5(3x - 4)}{(3x - 4)(4x + 1)}$$ 6. Expand the numerator: $$2(4x + 1) = 8x + 2$$ $$5(3x - 4) = 15x - 20$$ So numerator: $$8x + 2 - (15x - 20) = 8x + 2 - 15x + 20 = (8x - 15x) + (2 + 20) = -7x + 22$$ 7. The simplified expression is: $$\frac{-7x + 22}{(3x - 4)(4x + 1)}$$ 8. Final answer: Values found: $a = 4$, $b = 1$. Simplified expression: $$\frac{-7x + 22}{(3x - 4)(4x + 1)}$$