A scientist is modeling the growth rate VVV of a bacterial colony in terms of the concentration of a specific nutrient xxx. The relationship for x>0x > 0x>0 and x≠49x \neq 49x=49 is given by:
V=10.5+7x−1.5x12−x327−x V = \frac{10.5 + 7x - 1.5x^{\frac{1}{2}} - x^{\frac{3}{2}}}{7 - \sqrt{x}} V=7−x10.5+7x−1.5x21−x23Fully simplify the expression for VVV, justifying each step of your factorisation.
532 exam-style questions on AQA A Level Maths 1.5 B: Algebra and functions, covering 1.5.1 Laws of indices, 1.5.2 Surds, 1.5.3 Quadratic functions, 1.5.4 Simultaneous equations, 1.5.5 Linear and quadratic inequalities, 1.5.6 Polynomials and rational expressions, 1.5.7 Graphs of functions and proportion, 1.5.8 Composite and inverse functions (A-level only), 1.5.9 Transformations of graphs, 1.5.10 Partial fractions (A-level only), and 1.5.11 Functions in modelling (A-level only). Each one has a worked solution and a mark scheme showing where the marks go.