Gemcitabine Hydrochloride and Cisplatin With or Without Nab-Paclitaxel in Treating Patients With Newly Diagnosed Advanced Biliary Tract Cancers

Inclusion Criteria: * Patients must have histologically or cytologically confirmed intrahepatic cholangiocarcinoma, extrahepatic cholangiocarcinoma, or gallbladder cancer * NOTE: Pathology report must be uploaded in Rave. Histology report must be consistent with an adenocarcinoma with pancreaticobiliary primary assuming there are no pancreatic lesions and other primaries are ruled out per local standard * Patients must have documented metastatic or locally advanced unresectable disease on computed tomography (CT) or magnetic resonance (MR) imaging CT scans or MRIs used to assess measurable disease. Must have been completed within 28 days prior to registration. CT scans or MRIs used to assess non-measurable disease must have been completed within 42 days prior to registration. All disease must be assessed and documented on the Baseline Tumor Assessment Form * Patient must not have a current diagnosis of ampullary cancer * Patients must not have received prior systemic therapy for the current metastatic or locally advanced biliary cancer * Patient must not have received adjuvant therapy within 6 months prior to registration * Patients must have a complete medical history and physical exam within 28 days prior to registration * Patients must have a Zubrod performance status of 0 or 1 * Patients must not have a history of peripheral neuropathy of grade 2 or greater by Common Terminology Criteria for Adverse Events (CTCAE) 5.0. In CTCAE version 5.0 grade 2 sensory neuropathy is defined as ?moderate symptoms; limiting instrumental activities of daily living (ADLs)? * Absolute neutrophil count (ANC) \>= 1,500/mcL (obtained within 28 days prior to registration) * Platelets \>= 100,000/mcL (obtained within 28 days prior to registration) * Hemoglobin \>= 8 g/dL (obtained within 28 days prior to registration) * Serum albumin \>= 2.8 g/dL (obtained within 28 days prior to registration) * Total bilirubin =\< 1.5 x institutional upper limit of normal (IULN) (except patients with Gilbert?s syndrome, who must have a direct bilirubin \< 1.5 mg/dL) (obtained within 28 days prior to registration) * Serum glutamic-oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) and serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 8 x IULN (obtained within 28 days prior to registration) * Serum creatinine =\< IULN OR calculated creatinine clearance \>= 60 mL/min (obtained within 28 days prior to registration) * Patients must have CA19-9 obtained within 42 days prior to registration * Patients must have sodium, potassium, bicarbonate, chloride, blood urea nitrogen (BUN), calcium, total protein, magnesium, and alkaline phosphatase obtained within 28 days prior to registration * Patients must not have an active infection requiring systemic therapy * No other prior malignancy is allowed except for the following: adequately treated basal cell or squamous cell skin cancer, in situ cervical cancer, adequately treated stage I or II cancer from which the patient is currently in complete remission, or any other cancer from which the patient has been disease free for two years * Patients must not be pregnant or nursing. Women/men of reproductive potential must have agreed to use an effective contraceptive method. A woman is considered to be of "reproductive potential" if she has had menses at any time in the preceding 12 consecutive months. In addition to routine contraceptive methods, "effective contraception" also includes heterosexual celibacy and surgery intended to prevent pregnancy (or with a side-effect of pregnancy prevention) defined as a hysterectomy, bilateral oophorectomy or bilateral tubal ligation. However, if at any point a previously celibate patient chooses to become heterosexually active during the time period for use of contraceptive measures outlined in the protocol, he/she is responsible for beginning contraceptive measures * Sites must seek additional patient consent for the future use of specimens * Patients must be informed of the investigational nature of this study and must sign and give written informed consent in accordance with institutional and federal guidelines * As a part of the Oncology Patient Enrollment Network (OPEN) registration process the treating institution's identity is provided in order to ensure that the current (within 365 days) date of institutional review board approval for this study has been entered in the system